SAT Math - How to find the volume of a cube

Find the volume of a cube given side length is 1.

Explanation

To solve, simply use the formula for the volume of a cube. Thus,

What is the volume of a cube with a side length of 7.5 cm?

(Round two the nearest two places)

Explanation

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.

$\V=(7.5)^3 \V=(7.5)(7.5)(7.5) \V=421.875\approx 421.88cm^3$

If the volume of a cube is 50 cubic feet, what is the volume when the sides double in length?

100 cu ft

200 cu ft

300 cu ft

400 cu ft

500 cu ft

Explanation

Using S as the side length in the original cube, the original is s*s*s. Doubling one side and tripling the other gives 2s*2s*2s for a new volume formula for 8s*s*s, showing that the new volume is 8x greater than the original.

Find the volume of a cube whose side length is 7cm.

Explanation

The volume of a cube is length*width*height. In a cube all the side lengths are equal. Volume=7cm*7cm*7cm=343cm^3

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?

Explanation

Volume is calculated by height x width x length: $V=h\cdot w \cdot l$

For a cube, the height, width, and length are all the same value, so the equation can be simplified to , where is the length of one edge of the cube.

We know that for the initial cube, , so we can substitute this into the volume equation and solve for the length of one of the cube's sides:

$\sqrt[3]8=\sqrt[3]{s^3}$

So, one edge of the initial cube is long. When doubled, the cube will have edges that are each long. We can solve for the final volume of the cube by substituting into the equation for the volume of a cube and solving:

$V=4\cdot 4\cdot 4=64:cm^3$

How many smaller boxes with a dimensions of 1 by 5 by 5 can fit into cube shaped box with a surface area of 150?

Explanation

There surface are of a cube is 6 times the area of one face of the cube , therefore $6a^{2}=150$

$a^{2}=25$

$a=5$

a is equal to an edge of the cube

the volume of the cube is $a^{3}=5^{3}=125$

The problem states that the dimensions of the smaller boxes are 1 x 5 x 5, the volume of one of the smaller boxes is 25.

Therefore, 125/25 = 5 small boxes

At your university there is a metal cube-shaped sculpture near the math building. If the cube has a side length of 4 meters, what is the cube's volume?

Explanation

At your university there is a metal cube-shaped sculpture near the math building. If the cube has a side length of 4 meters, what is the cube's volume?

Begin with the formula for volume of a cube, then just simplify:

$V_{cube}=s^3=(4m)^3=64m^3$