Question

The volume of a pyramid that fits exactly inside a cube is 10 cubic feet what is the volume of a cube

Answer 1

(a^3/3)(3)=10(3)
a^3=30
volume=30

Answer 2

Answer:

$30\text{ ft}^3$

Step-by-step explanation:

We have been given that the volume of a pyramid that fits exactly inside a cube is 10 cubic feet. We are asked to find the volume of the cube.

We will use volume of cube and volume of pyramid formula to solve our given problem.

$\text{Volume of cube}=a^3$, where a represents the length of each side of the cube.

$\text{Volume of pyramid}=\frac{l*w*h}{3}$, where,

$l=\text{Length of the base of pyramid}$,

$w=\text{Width of the base of pyramid}$,

$h=\text{Height of pyramid}$.

Since the given pyramid fits inside the cube, so its length, width and height will be equal to each side of cube.

Let us assume that each side of our given cube is a units, so the volume of pyramid that fits inside the cube will be:

$\text{Volume of pyramid}=\frac{a*a*a}{3}$

$\text{Volume of pyramid}=\frac{a^3}{3}$

Upon substituting the value of pyramid's volume we will get,

$10\text{ ft}^3=\frac{a^3}{3}$

Since volume of cube equals $a^3$, so let us multiply both sides of our equation by 3 to solve for the volume of cube.

$10\text{ ft}^3\times 3=\frac{a^3}{3}\times 3$

$30\text{ ft}^3=a^3$

Therefore, the volume of our cube will be 30 cubic feet.