Question

the volume of a pyramid that fits exactly inside a cube is 9 cubic feet. what is the volume of the cube? 3 cubic feet 6 cubic feet 18 cubic feet 27 cubic feet

Explanation:

Step1: Recall volume - relationship

The volume formula for a pyramid with the same base and height as a cube is $V_{pyramid}=\frac{1}{3}V_{cube}$.

Step2: Solve for volume of cube

Given $V_{pyramid} = 9$ cubic - feet. Rearranging the formula $V_{pyramid}=\frac{1}{3}V_{cube}$ to solve for $V_{cube}$, we get $V_{cube}=3\times V_{pyramid}$.
Substitute $V_{pyramid}=9$ into the formula: $V_{cube}=3\times9 = 27$ cubic - feet.

Answer:

27 cubic feet