Question

The volume of a pyramid that fits exactly inside a cube is 49 cubic feet. What is the volume of the cube?

Answer 1

The volume of a pyramid is 1/3 the volume of the cube mentioned in the question since it fits exactly inside it. So multiply 49*3 = 147 cubic feet...

Hope this helped... :)

Answer 2

Answer:

B. $147\text{ ft}^3$

Step-by-step explanation:

We have been given that volume of a pyramid that fits exactly inside a cube is 49 cubic feet. We are asked to find the volume of the cube.

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

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

$\text{Volume of pyramid}=\frac{lwh}{3}$, where,

l = Length of pyramid,

w = Width of pyramid,

h = Height of pyramid.

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

$49\text{ ft}^3=\frac{a*a*a}{3}$

$49\text{ ft}^3=\frac{a^3}{3}$

Multiplying both sides of our equation by 3, we will get:

$3*49\text{ ft}^3=\frac{a^3}{3}*3$

$147\text{ ft}^3=a^3$

Therefore, the volume of cube is $147\text{ ft}^3$ and option B is the correct choice.