DSQ: Calculating the volume of a cube - GMAT Quantitative

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.