Cubes - GMAT Quantitative
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What is the length of the edge of a cube?
-
Its volume is 1,728 cubic meters.
-
Its surface area is 864 square meters
What is the length of the edge of a cube?
-
Its volume is 1,728 cubic meters.
-
Its surface area is 864 square meters
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Call the sidelength, surface area, and volume of the cube 
, 
, and 
, respectively.
Then
or, equivalently,
So, given statement 1 alone - that is, given only the volume, you can demonstrate the sidelength to be
Also,
or, equivalently,
Given statement 2 alone - that is, given only the surface area, you can demonstrate the sidelength to be
Therefore, the answer is that either statement alone is sufficient.
Call the sidelength, surface area, and volume of the cube
Then
or, equivalently,
So, given statement 1 alone - that is, given only the volume, you can demonstrate the sidelength to be
Also,
or, equivalently,
Given statement 2 alone - that is, given only the surface area, you can demonstrate the sidelength to be
Therefore, the answer is that either statement alone is sufficient.
A sphere is inscribed inside a cube. What is the volume of the sphere?
Statement 1: The surface area of the cube is 216.
Statement 2: The volume of the cube is 216.
A sphere is inscribed inside a cube. What is the volume of the sphere?
Statement 1: The surface area of the cube is 216.
Statement 2: The volume of the cube is 216.
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The diameter of a sphere inscribed inside a cube is equal to the length of one of the edges of a cube. From either the surface area or the volume of a cube, the appropriate formula can be used to calculate this length. Half this is the radius, from which the formula 
can be used to find the volume of the sphere.
The diameter of a sphere inscribed inside a cube is equal to the length of one of the edges of a cube. From either the surface area or the volume of a cube, the appropriate formula can be used to calculate this length. Half this is the radius, from which the formula
What is the length of edge 
of cube 
?
(1) 
.
(2) 
.
What is the length of edge
(1)
(2)
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In order to find the length of an edge, we would need any information about one of the faces of the cube or about the diagonal of the cube.
Statement 1 gives us the length of the diagonal of the cube, since the formula for the diagonal is 
where 
is the length of an edge of the cube and 
is the length of the diagonal we are able to find the length of the edge. Therefore statement 1 alone is sufficient.
Statement 2 alones is insufficient, it gives us something we can already tell knowing that ABCDEFGH is a cube.
Statement 1 alone is sufficient.
In order to find the length of an edge, we would need any information about one of the faces of the cube or about the diagonal of the cube.
Statement 1 gives us the length of the diagonal of the cube, since the formula for the diagonal is
Statement 2 alones is insufficient, it gives us something we can already tell knowing that ABCDEFGH is a cube.
Statement 1 alone is sufficient.
is a cube. What is the length of edge 
?
(1) The volume of the cube is 
.
(2) The area of face 
is 
.
(1) The volume of the cube is
(2) The area of face
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Like we have previously seen, to find the length of an edge, we need to have information about the other faces or anything else within the cube.
Statement 1 tells us that the volume of the cube is 
, from this we can find the length of the side of the cube. Statement 1 alone is sufficient.
Statement 2, tells us that the area of ABCD is 
, similarily, by taking the square root of this number, we can find the length of the edge of the cube.
Therefore each statement alone is sufficient.
Like we have previously seen, to find the length of an edge, we need to have information about the other faces or anything else within the cube.
Statement 1 tells us that the volume of the cube is
Statement 2, tells us that the area of ABCD is
Therefore each statement alone is sufficient.
Find the length of an edge of the cube.
- The volume of the cube is
.
- The surface area of the cube is
.
Find the length of an edge of the cube.
- The volume of the cube is
- The surface area of the cube is
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Statement 1: Use the volume formula for a cube to solve for the side length.
where 
represents the length of the edge
Statement 2: Use the surface area formula for a cube to solve for the side length.
Each statement alone is sufficient to answer the question.
Statement 1: Use the volume formula for a cube to solve for the side length.
Statement 2: Use the surface area formula for a cube to solve for the side length.
Each statement alone is sufficient to answer the question.
Ron is making a box in the shape of a cube. He needs to know how much wood he needs. Find the surface area of the box.
I) The diagonal distance across the box will be equivalent to 
.
II) Half the length of one side is 
.
Ron is making a box in the shape of a cube. He needs to know how much wood he needs. Find the surface area of the box.
I) The diagonal distance across the box will be equivalent to
II) Half the length of one side is
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To find the surface area of a cube, we need the length of one side.
Statement I gives the diagonal, we can use this to find the length of one side.
Statement II gives us a clue about the length of one side; we can use that to find the full length of one side.
The following formula gives us the surface area of a cube:
Use Statement I to find the length of the side with the following formula, where 
is the diagonal and 
is the side length:
So, using Statement I, we find the surface area to be
Using Statement, we get that the length of one side is two times two:
Again, use the surface area formula to get the following:
To find the surface area of a cube, we need the length of one side.
Statement I gives the diagonal, we can use this to find the length of one side.
Statement II gives us a clue about the length of one side; we can use that to find the full length of one side.
The following formula gives us the surface area of a cube:
Use Statement I to find the length of the side with the following formula, where
So, using Statement I, we find the surface area to be
Using Statement, we get that the length of one side is two times two:
Again, use the surface area formula to get the following:
Find the volume of the cube.
1. The cube has a diagonal of 17.32 inches.
2. The cube has a surface area of 600 square inches.
Find the volume of the cube.
1. The cube has a diagonal of 17.32 inches.
2. The cube has a surface area of 600 square inches.
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To find the volume of a cube, we only need the length of one side. Using statement 1, we can figure out the length of a side based on the diagonal. We can use the figure below to find the ratio of the diagonal to one side. If the we let the length of one side be x, we can use Pythagorean's theorem to find the length of the diagonal. So, in triangle BCD, we have a right triangle, with two sides of length x. We can set up the equation that the length of BD is 
.
Then we can see triangle ADB is also a right triangle. Using Pythagorean's theorem we get the length of AB is 
.
So, if we divide the number from statement 1 by the square root of 3, we get the length of each side of the cube. Doing this, we get 
. Thus, we can solve this problem with just the information from statement 1.
Now, we can also check statement 2. If we know the surface area of the cube, we can use that information to find the length of each side of the cube. We know that the surface area of a cube is the sum of the six faces of the cube, which all have equal area and are all squares. We can divide the total surface area by 6 to find the surface area of each square face. So, 600/6 = 100. We know that the area of a square is just the length of one side squared, so we can take the square root of 100 to find that the length of each side is 10. Thus statement 2 is also sufficient to solve this problem.
Therefore, the answer is that either statement alone is sufficient to answer the question.
To find the volume of a cube, we only need the length of one side. Using statement 1, we can figure out the length of a side based on the diagonal. We can use the figure below to find the ratio of the diagonal to one side. If the we let the length of one side be x, we can use Pythagorean's theorem to find the length of the diagonal. So, in triangle BCD, we have a right triangle, with two sides of length x. We can set up the equation that the length of BD is
Then we can see triangle ADB is also a right triangle. Using Pythagorean's theorem we get the length of AB is
So, if we divide the number from statement 1 by the square root of 3, we get the length of each side of the cube. Doing this, we get
Now, we can also check statement 2. If we know the surface area of the cube, we can use that information to find the length of each side of the cube. We know that the surface area of a cube is the sum of the six faces of the cube, which all have equal area and are all squares. We can divide the total surface area by 6 to find the surface area of each square face. So, 600/6 = 100. We know that the area of a square is just the length of one side squared, so we can take the square root of 100 to find that the length of each side is 10. Thus statement 2 is also sufficient to solve this problem.
Therefore, the answer is that either statement alone is sufficient to answer the question.
How much does a cube weigh?
Statement 1: The cube is made of material that weighs 3 pounds per cubic foot.
Statement 2: Each face of the cube is a square with area 16 square feet.
How much does a cube weigh?
Statement 1: The cube is made of material that weighs 3 pounds per cubic foot.
Statement 2: Each face of the cube is a square with area 16 square feet.
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The weight of a cube is dependent on its density in pounds per cubic foot and its volume in cubic feet. We need Statement 1 for the density. Statement 2 is needed for the volume - and it gives us the means to find it, since we can take the square root of the area of one side, 16, to get sidelength 4 feet, and we can cube that to get the volume of 64 cubic feet. Now we can multiply 64 cubic feet by 3 pounds per cubic foot to get 192 pounds.
The weight of a cube is dependent on its density in pounds per cubic foot and its volume in cubic feet. We need Statement 1 for the density. Statement 2 is needed for the volume - and it gives us the means to find it, since we can take the square root of the area of one side, 16, to get sidelength 4 feet, and we can cube that to get the volume of 64 cubic feet. Now we can multiply 64 cubic feet by 3 pounds per cubic foot to get 192 pounds.
Find the volume of cube W.
I) The base of W has an area of 
leagues squared.
II) The diagonal of the base of W has a length of 
leagues.
Find the volume of cube W.
I) The base of W has an area of
II) The diagonal of the base of W has a length of
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If we know the base of W, we can find the side length. We then cube the side length to find the volume of a square.
If we know the diagonal of the base of W, we can find the side length. As outlined above, we can then cube the side length to find the volume.
Therefore either statement alone is sufficient to solve the question.
If we know the base of W, we can find the side length. We then cube the side length to find the volume of a square.
If we know the diagonal of the base of W, we can find the side length. As outlined above, we can then cube the side length to find the volume.
Therefore either statement alone is sufficient to solve the question.
Calculate the volume of a cube.
- The length of the cube's edge is
.
- The surface area of the cube is
.
Calculate the volume of a cube.
- The length of the cube's edge is
- The surface area of the cube is
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Statement 1: We need the length of the edge of the cube to calculate the volume. In this statement we're provided with the length so we just need to plug it into the equation for a cube's volume.
Statement 2: In this case, we need to solve for the length of the cube's edge which we can easily do:
Now that we have our length, we can calculate the volume.
Statement 1: We need the length of the edge of the cube to calculate the volume. In this statement we're provided with the length so we just need to plug it into the equation for a cube's volume.
Statement 2: In this case, we need to solve for the length of the cube's edge which we can easily do:
Now that we have our length, we can calculate the volume.
A lab has designed a cube to help with their testing procedures. Find the volume of the cube.
I) The cube will have a side length of 
meters.
II) The cube will have a diagonal of 
meters.
A lab has designed a cube to help with their testing procedures. Find the volume of the cube.
I) The cube will have a side length of
II) The cube will have a diagonal of
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Recall that the volume of a cube is equal to the cube of its side length, and that the diagonal of a cube is equal to 
length.
I) Use the following:
II) Gives us the diagonal. Divide by the square root of three, then cube it!
Either statement is sufficient to answer the question.
Recall that the volume of a cube is equal to the cube of its side length, and that the diagonal of a cube is equal to
I) Use the following:
II) Gives us the diagonal. Divide by the square root of three, then cube it!
Either statement is sufficient to answer the question.
Find the volume of the cube.
1. The cube has a diagonal of 17.32 inches.
2. The cube has a surface area of 600 square inches.
Find the volume of the cube.
1. The cube has a diagonal of 17.32 inches.
2. The cube has a surface area of 600 square inches.
Tap to see back →
To find the volume of a cube, we only need the length of one side. Using statement 1, we can figure out the length of a side based on the diagonal. We can use the figure below to find the ratio of the diagonal to one side. If the we let the length of one side be x, we can use Pythagorean's theorem to find the length of the diagonal. So, in triangle BCD, we have a right triangle, with two sides of length x. We can set up the equation that the length of BD is .
Then we can see triangle ADB is also a right triangle. Using Pythagorean's theorem we get the length of AB is .
So, if we divide the number from statement 1 by the square root of 3, we get the length of each side of the cube. Doing this, we get . Thus, we can solve this problem with just the information from statement 1.
Now, we can also check statement 2. If we know the surface area of the cube, we can use that information to find the length of each side of the cube. We know that the surface area of a cube is the sum of the six faces of the cube, which all have equal area and are all squares. We can divide the total surface area by 6 to find the surface area of each square face. So, 600/6 = 100. We know that the area of a square is just the length of one side squared, so we can take the square root of 100 to find that the length of each side is 10. Thus statement 2 is also sufficient to solve this problem.
Therefore, the answer is that either statement alone is sufficient to answer the question.
To find the volume of a cube, we only need the length of one side. Using statement 1, we can figure out the length of a side based on the diagonal. We can use the figure below to find the ratio of the diagonal to one side. If the we let the length of one side be x, we can use Pythagorean's theorem to find the length of the diagonal. So, in triangle BCD, we have a right triangle, with two sides of length x. We can set up the equation that the length of BD is
Then we can see triangle ADB is also a right triangle. Using Pythagorean's theorem we get the length of AB is
So, if we divide the number from statement 1 by the square root of 3, we get the length of each side of the cube. Doing this, we get
Now, we can also check statement 2. If we know the surface area of the cube, we can use that information to find the length of each side of the cube. We know that the surface area of a cube is the sum of the six faces of the cube, which all have equal area and are all squares. We can divide the total surface area by 6 to find the surface area of each square face. So, 600/6 = 100. We know that the area of a square is just the length of one side squared, so we can take the square root of 100 to find that the length of each side is 10. Thus statement 2 is also sufficient to solve this problem.
Therefore, the answer is that either statement alone is sufficient to answer the question.
How much does a cube weigh?
Statement 1: The cube is made of material that weighs 3 pounds per cubic foot.
Statement 2: Each face of the cube is a square with area 16 square feet.
How much does a cube weigh?
Statement 1: The cube is made of material that weighs 3 pounds per cubic foot.
Statement 2: Each face of the cube is a square with area 16 square feet.
Tap to see back →
The weight of a cube is dependent on its density in pounds per cubic foot and its volume in cubic feet. We need Statement 1 for the density. Statement 2 is needed for the volume - and it gives us the means to find it, since we can take the square root of the area of one side, 16, to get sidelength 4 feet, and we can cube that to get the volume of 64 cubic feet. Now we can multiply 64 cubic feet by 3 pounds per cubic foot to get 192 pounds.
The weight of a cube is dependent on its density in pounds per cubic foot and its volume in cubic feet. We need Statement 1 for the density. Statement 2 is needed for the volume - and it gives us the means to find it, since we can take the square root of the area of one side, 16, to get sidelength 4 feet, and we can cube that to get the volume of 64 cubic feet. Now we can multiply 64 cubic feet by 3 pounds per cubic foot to get 192 pounds.
Find the volume of cube W.
I) The base of W has an area of leagues squared.
II) The diagonal of the base of W has a length of leagues.
Find the volume of cube W.
I) The base of W has an area of
II) The diagonal of the base of W has a length of
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If we know the base of W, we can find the side length. We then cube the side length to find the volume of a square.
If we know the diagonal of the base of W, we can find the side length. As outlined above, we can then cube the side length to find the volume.
Therefore either statement alone is sufficient to solve the question.
If we know the base of W, we can find the side length. We then cube the side length to find the volume of a square.
If we know the diagonal of the base of W, we can find the side length. As outlined above, we can then cube the side length to find the volume.
Therefore either statement alone is sufficient to solve the question.
Calculate the volume of a cube.
- The length of the cube's edge is .
- The surface area of the cube is .
Calculate the volume of a cube.
- The length of the cube's edge is
- The surface area of the cube is
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Statement 1: We need the length of the edge of the cube to calculate the volume. In this statement we're provided with the length so we just need to plug it into the equation for a cube's volume.
Statement 2: In this case, we need to solve for the length of the cube's edge which we can easily do:
Now that we have our length, we can calculate the volume.
Statement 1: We need the length of the edge of the cube to calculate the volume. In this statement we're provided with the length so we just need to plug it into the equation for a cube's volume.
Statement 2: In this case, we need to solve for the length of the cube's edge which we can easily do:
Now that we have our length, we can calculate the volume.
A lab has designed a cube to help with their testing procedures. Find the volume of the cube.
I) The cube will have a side length of meters.
II) The cube will have a diagonal of meters.
A lab has designed a cube to help with their testing procedures. Find the volume of the cube.
I) The cube will have a side length of
II) The cube will have a diagonal of
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Recall that the volume of a cube is equal to the cube of its side length, and that the diagonal of a cube is equal to length.
I) Use the following:
II) Gives us the diagonal. Divide by the square root of three, then cube it!
Either statement is sufficient to answer the question.
Recall that the volume of a cube is equal to the cube of its side length, and that the diagonal of a cube is equal to
I) Use the following:
II) Gives us the diagonal. Divide by the square root of three, then cube it!
Either statement is sufficient to answer the question.
Find the volume of the cube.
1. The cube has a diagonal of 17.32 inches.
2. The cube has a surface area of 600 square inches.
Find the volume of the cube.
1. The cube has a diagonal of 17.32 inches.
2. The cube has a surface area of 600 square inches.
Tap to see back →
To find the volume of a cube, we only need the length of one side. Using statement 1, we can figure out the length of a side based on the diagonal. We can use the figure below to find the ratio of the diagonal to one side. If the we let the length of one side be x, we can use Pythagorean's theorem to find the length of the diagonal. So, in triangle BCD, we have a right triangle, with two sides of length x. We can set up the equation that the length of BD is .
Then we can see triangle ADB is also a right triangle. Using Pythagorean's theorem we get the length of AB is .
So, if we divide the number from statement 1 by the square root of 3, we get the length of each side of the cube. Doing this, we get . Thus, we can solve this problem with just the information from statement 1.
Now, we can also check statement 2. If we know the surface area of the cube, we can use that information to find the length of each side of the cube. We know that the surface area of a cube is the sum of the six faces of the cube, which all have equal area and are all squares. We can divide the total surface area by 6 to find the surface area of each square face. So, 600/6 = 100. We know that the area of a square is just the length of one side squared, so we can take the square root of 100 to find that the length of each side is 10. Thus statement 2 is also sufficient to solve this problem.
Therefore, the answer is that either statement alone is sufficient to answer the question.
To find the volume of a cube, we only need the length of one side. Using statement 1, we can figure out the length of a side based on the diagonal. We can use the figure below to find the ratio of the diagonal to one side. If the we let the length of one side be x, we can use Pythagorean's theorem to find the length of the diagonal. So, in triangle BCD, we have a right triangle, with two sides of length x. We can set up the equation that the length of BD is
Then we can see triangle ADB is also a right triangle. Using Pythagorean's theorem we get the length of AB is
So, if we divide the number from statement 1 by the square root of 3, we get the length of each side of the cube. Doing this, we get
Now, we can also check statement 2. If we know the surface area of the cube, we can use that information to find the length of each side of the cube. We know that the surface area of a cube is the sum of the six faces of the cube, which all have equal area and are all squares. We can divide the total surface area by 6 to find the surface area of each square face. So, 600/6 = 100. We know that the area of a square is just the length of one side squared, so we can take the square root of 100 to find that the length of each side is 10. Thus statement 2 is also sufficient to solve this problem.
Therefore, the answer is that either statement alone is sufficient to answer the question.
How much does a cube weigh?
Statement 1: The cube is made of material that weighs 3 pounds per cubic foot.
Statement 2: Each face of the cube is a square with area 16 square feet.
How much does a cube weigh?
Statement 1: The cube is made of material that weighs 3 pounds per cubic foot.
Statement 2: Each face of the cube is a square with area 16 square feet.
Tap to see back →
The weight of a cube is dependent on its density in pounds per cubic foot and its volume in cubic feet. We need Statement 1 for the density. Statement 2 is needed for the volume - and it gives us the means to find it, since we can take the square root of the area of one side, 16, to get sidelength 4 feet, and we can cube that to get the volume of 64 cubic feet. Now we can multiply 64 cubic feet by 3 pounds per cubic foot to get 192 pounds.
The weight of a cube is dependent on its density in pounds per cubic foot and its volume in cubic feet. We need Statement 1 for the density. Statement 2 is needed for the volume - and it gives us the means to find it, since we can take the square root of the area of one side, 16, to get sidelength 4 feet, and we can cube that to get the volume of 64 cubic feet. Now we can multiply 64 cubic feet by 3 pounds per cubic foot to get 192 pounds.
Find the volume of cube W.
I) The base of W has an area of leagues squared.
II) The diagonal of the base of W has a length of leagues.
Find the volume of cube W.
I) The base of W has an area of
II) The diagonal of the base of W has a length of
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If we know the base of W, we can find the side length. We then cube the side length to find the volume of a square.
If we know the diagonal of the base of W, we can find the side length. As outlined above, we can then cube the side length to find the volume.
Therefore either statement alone is sufficient to solve the question.
If we know the base of W, we can find the side length. We then cube the side length to find the volume of a square.
If we know the diagonal of the base of W, we can find the side length. As outlined above, we can then cube the side length to find the volume.
Therefore either statement alone is sufficient to solve the question.
Calculate the volume of a cube.
- The length of the cube's edge is .
- The surface area of the cube is .
Calculate the volume of a cube.
- The length of the cube's edge is
- The surface area of the cube is
Tap to see back →
Statement 1: We need the length of the edge of the cube to calculate the volume. In this statement we're provided with the length so we just need to plug it into the equation for a cube's volume.
Statement 2: In this case, we need to solve for the length of the cube's edge which we can easily do:
Now that we have our length, we can calculate the volume.
Statement 1: We need the length of the edge of the cube to calculate the volume. In this statement we're provided with the length so we just need to plug it into the equation for a cube's volume.
Statement 2: In this case, we need to solve for the length of the cube's edge which we can easily do:
Now that we have our length, we can calculate the volume.