Question

A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the height of the prism is placed inside the prism, as shown in the figure.

The volume of the space outside the pyramid but inside the prism is how many cubic centimeters ?

Answer 1

`250\ cm^3`

Explanation:

A rectangular prism has

• a height of 12 centimeters
• a square base with sides measuring 5 centimeters.

The volume of the prism is

`V_(prism)=A_(base)\cdot H,\\ \\V=5^2\cdot 12=25\cdot 12=300\ cm^3`

A pyramid with has

• the same base as the prism
• half the height of the prism

The volume of the pyramid is

`V_(pyramid)=(1)/(3)\cdot A_(base)\cdot h,\\ \\h=(H)/(2)=(12)/(2)=6\ cm,\\ \\V_(pyramid)=(1)/(3)\cdot 5^2\cdot 6=(1)/(3)\cdot 25\cdot 6=50\ cm^3`

The volume of the space outside the pyramid but inside the prism is

`V=V_(prism)-V_(pyramid)=300-50=250\ cm^3`