GMAT Quantitative › Calculating the volume of a cube
The distance from one vertex of a cube to its opposite vertex is twelve feet. Give the volume of the cube.
Since we are looking at yards, we will look at twelve feet as four yards.
Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
yards.
Cube this sidelength to get the volume:
cubic yards.
A sphere with surface area is inscribed inside a cube. Give the volume of the cube.
The sidelength of the cube is the diameter of the inscribed sphere, which is twice that sphere's radius. The sphere has surface area , so the radius is calculated as follows:
The diameter of the sphere - and the sidelength of the cube - is twice this, or .
Cube this sidelength to get the volume of the cube:
An aquarium is shaped like a perfect cube; the area of each glass face is square meters. If it is filled to the recommended
capacity, then how much water will it contain?
Note: cubic meter
liters.
The correct answer is not given among the other choices.
A perfect cube has square faces; if a face has area 6.25 square meters, then each side of each face measures the square root of this, or 2.5 meters. The volume of the tank is the cube of this, or
cubic meters.
Its capacity in liters is liters.
80% of this is
liters.
Which choice comes closest to the volume of a cube with surface area square centimeters?
The suface area of a cube is six times the square of the length of one side, so solve for in the following:
This is the sidelength in centimeters; since we are looking at meters, divide this by 100 to convert to meters.
Cube this to get volume
cubic meters.
Of the given choices, 3.5 cubic meters comes closest.
The length of a diagonal of a cube is . Give the volume of the cube.
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:
The length of a diagonal of one face of a cube is . Give the volume of the cube.
The correct answer is not among the other responses.
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 cube is inscribed inside a sphere with volume . Give the volume of the cube.
The correct answer is not given among the other responses.
The diameter of the circle - twice its radius - coincides with the length of a diagonal of the inscribed cube. The sphere has volume , so the radius is calculated as follows:
The diameter of the sphere - and the length of a diagonal of the cube - is twice this, or 6.
Now, let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,
The volume of the cube is the cube of this, or
The distance from one vertex of a cube to its opposite vertex is one foot. Give the volume of the cube.
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.
A cube has a volume of cubic feet. If the length of each side of the cube is doubled, what is its new volume, in cubic feet?
One way we can solve this problem is by first determining the dimensions of the original cube. By definition, the length, width, and depth of a cube are equal, so if the original volume is 8 cubic feet, then:
We then double the length of each side of the original cube, so the length of each side of the new cube is:
Now we can use the dimensions of our new cube to find its volume:
So if we double the dimensions of the original cube, the resulting cube has a volume that is eight times greater, 64 cubic feet.
A sphere with surface area circumscribes a cube. Give the volume of the cube.
The correct answer is not given among the other responses.
The diameter of a sphere is equal to the length of a diagonal of the cube it circumscribes. We can derive the radius using the formula for the volume of a sphere, but first, we have to solve for the radius using the formula for the surface area of a sphere:
The diameter is twice this, or . This is the length of the diagonal of the cube. By the three-dimensional extension of the Pythagorean Theorem,
The volume is the cube of this:
, which is not given as one of the choices.