SAT Math : How to find the volume of a cube
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Example Question #11 : How To Find The Volume Of A Cube
A cube is inscribed inside a sphere of radius 1 such that each of the eight vertices of the cube lie on the surface of the sphere. What is the volume of the cube?
To make this problem easier to solve, we can inscribe a smaller square in the cube. In the diagram above, points 
Using the Pythagorean Theorem, we can now solve for 
Since the side of the inscribed cube is 
Example Question #31 : Solid Geometry
A perfect cube has a volume of 8 cubic centimeters. If the height, length and width of the cube were doubled, what would be the volume of the cube?
Volume is calculated by height x width x length:
For a cube, the height, width, and length are all the same value, so the equation can be simplified to 
We know that for the initial cube, 
So, one edge of the initial cube is 
Example Question #731 : Geometry
What's the volume of a cube with a length of 
Write the volume formula for a cube.
Substitute the side.
Example Question #732 : Geometry
If the surface area of a cube is 30, what is the volume of the cube?
Write the surface area formula of the cube.
Substitute the surface area and find the side.
Write the volume for the cube.
Substitute the side to the volume formula.
Example Question #14 : How To Find The Volume Of A Cube
The volumes of six cubes form an arithmetic sequence. The two smallest cubes have sidelengths 10 and 12, respectively. Give the volume of the largest cube.
The volume of a cube is equal to the length of a side raised to the third power. The two smallest cubes will have volumes:
and
respectively.
The volumes form an arithmetic sequence with these two volumes as the first two terms, so their common difference is
The volume of the largest, or sixth-smallest, cube, is
Example Question #41 : Solid Geometry
Find the volume of a cube with side length 4.
To solve, simply use the formula for the volume of a cube.
Substitute in the side length of four into the following equation.
Thus,
Example Question #731 : Geometry
Find the volume of a cube given side length is 1.
To solve, simply use the formula for the volume of a cube. Thus,
Example Question #41 : Cubes
A cube has a surface area of 
Remember that a cube's surface area, because it's comprised of six identical squares, can be stated as 
The last step is easy:
Example Question #11 : How To Find The Volume Of A Cube
What is the volume of a cube with a side length of 7.5 cm?
(Round two the nearest two places)
The formula for volume of a cube is,
where
The side length of the cube is given as 7.5cm.
Substituting this into the formula for a cube's volume is as follows.
Example Question #42 : Cubes
Find the volume of a cube whose side length is 7cm.
The volume of a cube is length*width*height. In a cube all the side lengths are equal. Volume=7cm*7cm*7cm=343cm^3
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