How to find the volume of a cube - SSAT Upper Level Quantitative
Card 1 of 52
A cube has six square faces, each with area 64 square inches. Using the conversion factor 1 inch = 2.5 centimeters, give the volume of this cube in cubic centimeters, rounding to the nearest whole number.
A cube has six square faces, each with area 64 square inches. Using the conversion factor 1 inch = 2.5 centimeters, give the volume of this cube in cubic centimeters, rounding to the nearest whole number.
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The volume of a cube is the cube of its sidelength, which is also the sidelength of each square face. This sidelength is the square root of the area 64:
inches.
Multiply this by 2.5 to get the sidelength in centimeters:
centimeters.
The cube of this is
cubic centimeters
The volume of a cube is the cube of its sidelength, which is also the sidelength of each square face. This sidelength is the square root of the area 64:
Multiply this by 2.5 to get the sidelength in centimeters:
The cube of this is
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A cube has a side length of 5 inches. Give the volume and surface area of the cube.
A cube has a side length of 5 inches. Give the volume and surface area of the cube.
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A cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. As a formula:
where 
is the length of any edge of the cube.
The Surface Area of a cube can be calculated as 
.
So we get:
Volume 
Surface area
A cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. As a formula:
The Surface Area of a cube can be calculated as
So we get:
Volume
Surface area
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A cheese seller has a 2 foot x 2 foot x 2 foot block of gouda and she wants to cut it into smaller gouda cubes that are 1.5 inches on a side. How many cubes can she cut?
A cheese seller has a 2 foot x 2 foot x 2 foot block of gouda and she wants to cut it into smaller gouda cubes that are 1.5 inches on a side. How many cubes can she cut?
Tap to reveal answer
First we need to determine how many of the small cubes of gouda would fit along one dimension of the large cheese block. One edge of the large block is 24 inches, so 16 smaller cubes 
would fit along the edge. Now we simply cube this one dimension to see how many cubes fit within the whole cube. 
.
First we need to determine how many of the small cubes of gouda would fit along one dimension of the large cheese block. One edge of the large block is 24 inches, so 16 smaller cubes
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Give the volume of a cube with surface area 
.
Give the volume of a cube with surface area
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Let 
be the length of one edge of the cube. Since its surface area is 
, one face has one-sixth of this area, or 
. Therefore,
,
and
Cube this sidelength to get the volume:
Let
and
Cube this sidelength to get the volume:
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The distance from one vertex of a cube to its opposite vertex is 
. Give the volume of the cube.
The distance from one vertex of a cube to its opposite vertex is
Tap to reveal answer
Let 
be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
Cube this sidelength to get the volume:
Let
Cube this sidelength to get the volume:
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The length of a diagonal of one face of a cube is 10. Give the volume of the cube.
The length of a diagonal of one face of a cube is 10. Give the volume of the cube.
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Since a diagonal of a square face of the cube is 10, each side of each square has length 
times this, or 
.
Cube this to get the volume of the cube:
.
Since a diagonal of a square face of the cube is 10, each side of each square has length
Cube this to get the volume of the cube:
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The distance from one vertex of a cube to its opposite vertex is one foot. Give the volume of the cube in inches.
The distance from one vertex of a cube to its opposite vertex is one foot. Give the volume of the cube in inches.
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Since we are looking at inches, we will look at one foot as twelve inches.
Let 
be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
inches.
Cube this sidelength to get the volume:
cubic inches.
Since we are looking at inches, we will look at one foot as twelve inches.
Let
Cube this sidelength to get the volume:
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An aquarium is shaped like a perfect cube; the area of each glass face is 1.44 square meters. If it is filled to the recommended 90% capacity, then, to the nearest hundred liters, how much water will it contain?
Note: 1 cubic meter = 1,000 liters.
An aquarium is shaped like a perfect cube; the area of each glass face is 1.44 square meters. If it is filled to the recommended 90% capacity, then, to the nearest hundred liters, how much water will it contain?
Note: 1 cubic meter = 1,000 liters.
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A perfect cube has square faces; if a face has area 1.44 square meters, then each side of each face measures the square root of this, or 1.2 meters. The volume of the tank is the cube of this, or
cubic meters.
Its capacity in liters is 
liters.
90% of this is
liters.
This rounds to 1,600 liters, the correct response.
A perfect cube has square faces; if a face has area 1.44 square meters, then each side of each face measures the square root of this, or 1.2 meters. The volume of the tank is the cube of this, or
Its capacity in liters is
90% of this is
This rounds to 1,600 liters, the correct response.
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The distance from one vertex of a perfectly cubic aquarium to its opposite vertex is 
meters. Give the volume of the aquarium in liters.
cubic meter = 
liters.
The distance from one vertex of a perfectly cubic aquarium to its opposite vertex is
Tap to reveal answer
Let 
be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
meters.
Cube this sidelength to get the volume:
cubic meters.
To convert this to liters, multiply by 1,000:
liters.
Let
Cube this sidelength to get the volume:
To convert this to liters, multiply by 1,000:
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Give the volume of a cube with surface area 3 square meters.
Give the volume of a cube with surface area 3 square meters.
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Let be the length of one edge of the cube. Since its surface area is 3 square meters, one face has one-sixth of this area, or 
square meters. Therefore, 
, and 
meters.
The choices are in centimeters, so multiply this by 100 - the sidelength is
centimeters.
The volume is the cube of this, or 
cubic centimeters.
Let
The choices are in centimeters, so multiply this by 100 - the sidelength is
The volume is the cube of this, or
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The length of a diagonal of a cube is 
. Give the volume of the cube.
The length of a diagonal of a cube is
Tap to reveal answer
Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
Cube the sidelength to get the volume:
Let
Cube the sidelength to get the volume:
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The length of a diagonal of one face of a cube is 
. Give the volume of the cube.
The length of a diagonal of one face of a cube is
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A diagonal of a square has length 
times that of a side, so each side of each square face of the cube has length 
. Cube this to get the volume:
A diagonal of a square has length
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Find the volume of a cube with a side length of 
.
Find the volume of a cube with a side length of
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Write the formula for the volume of a cube.
The correct answer is 
.
Write the formula for the volume of a cube.
The correct answer is
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A cube has six square faces, each with area 64 square inches. Using the conversion factor 1 inch = 2.5 centimeters, give the volume of this cube in cubic centimeters, rounding to the nearest whole number.
A cube has six square faces, each with area 64 square inches. Using the conversion factor 1 inch = 2.5 centimeters, give the volume of this cube in cubic centimeters, rounding to the nearest whole number.
Tap to reveal answer
The volume of a cube is the cube of its sidelength, which is also the sidelength of each square face. This sidelength is the square root of the area 64:
inches.
Multiply this by 2.5 to get the sidelength in centimeters:
centimeters.
The cube of this is
cubic centimeters
The volume of a cube is the cube of its sidelength, which is also the sidelength of each square face. This sidelength is the square root of the area 64:
Multiply this by 2.5 to get the sidelength in centimeters:
The cube of this is
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A cube has a side length of 5 inches. Give the volume and surface area of the cube.
A cube has a side length of 5 inches. Give the volume and surface area of the cube.
Tap to reveal answer
A cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. As a formula:
where is the length of any edge of the cube.
The Surface Area of a cube can be calculated as .
So we get:
Volume
Surface area
A cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. As a formula:
The Surface Area of a cube can be calculated as
So we get:
Volume
Surface area
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A cheese seller has a 2 foot x 2 foot x 2 foot block of gouda and she wants to cut it into smaller gouda cubes that are 1.5 inches on a side. How many cubes can she cut?
A cheese seller has a 2 foot x 2 foot x 2 foot block of gouda and she wants to cut it into smaller gouda cubes that are 1.5 inches on a side. How many cubes can she cut?
Tap to reveal answer
First we need to determine how many of the small cubes of gouda would fit along one dimension of the large cheese block. One edge of the large block is 24 inches, so 16 smaller cubes would fit along the edge. Now we simply cube this one dimension to see how many cubes fit within the whole cube. .
First we need to determine how many of the small cubes of gouda would fit along one dimension of the large cheese block. One edge of the large block is 24 inches, so 16 smaller cubes
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Give the volume of a cube with surface area .
Give the volume of a cube with surface area
Tap to reveal answer
Let be the length of one edge of the cube. Since its surface area is , one face has one-sixth of this area, or . Therefore,
,
and
Cube this sidelength to get the volume:
Let
and
Cube this sidelength to get the volume:
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The distance from one vertex of a cube to its opposite vertex is . Give the volume of the cube.
The distance from one vertex of a cube to its opposite vertex is
Tap to reveal answer
Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
Cube this sidelength to get the volume:
Let
Cube this sidelength to get the volume:
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The length of a diagonal of one face of a cube is 10. Give the volume of the cube.
The length of a diagonal of one face of a cube is 10. Give the volume of the cube.
Tap to reveal answer
Since a diagonal of a square face of the cube is 10, each side of each square has length times this, or .
Cube this to get the volume of the cube:
.
Since a diagonal of a square face of the cube is 10, each side of each square has length
Cube this to get the volume of the cube:
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The distance from one vertex of a cube to its opposite vertex is one foot. Give the volume of the cube in inches.
The distance from one vertex of a cube to its opposite vertex is one foot. Give the volume of the cube in inches.
Tap to reveal answer
Since we are looking at inches, we will look at one foot as twelve inches.
Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
inches.
Cube this sidelength to get the volume:
cubic inches.
Since we are looking at inches, we will look at one foot as twelve inches.
Let
Cube this sidelength to get the volume:
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