Question

Type the correct answer in the box.

Answer 1

Answer:

$250\ cm^3$

Step-by-step explanation:

step 1

Find the volume of the prism

The volume of the prism is equal to

$V=LWH$

we have

$L=5\ cm\\W=5\ cm\\H=12\ cm$

substitute

$V=(5)(5)(12)=300\ cm^3$

step 2

Find the volume of the pyramid

The volume of the pyramid is

$V=\frac{1}{3}Bh$

where

B is the area of the base

$B=5^2=25\ cm^2$

$h=12/2=6\cm$ ---> half the height of the prism

substitute

$V=\frac{1}{3}(25)(6)=50\ cm^3$

step 3

we know that

The volume of the space outside the pyramid but inside the prism is equal to subtract the volume of the pyramid from the volume of the cylinder

$300\ cm^3-50\ cm^3=250\ cm^3$