Question

Both pyramids in the figure have the same base area as the prism. The ratio of the combined volume of the pyramids to the volume of the prism, expressed as a fraction in simplest form, is

Answer 1

Answer:

$ratio=\frac{1}{3}$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the volume of the two pyramids

we know that

The volume of the two pyramids is equal to

$V=2[\frac{1}{3}Bh]$

where

B is the area of the base

h is the height of the pyramid

step 2

Find the volume of the prism

Remember that

If the height of the pyramid is h, then the height of the prism is 2h

we know that

The volume of the prism is equal to

$V=B(H)$

we have

$H=2h$

$V=B(2h)$

$V=2Bh$

step 3

Find out the ratio of the combined volume of the pyramids to the volume of the prism

so

$ratio=\frac{2[\frac{1}{3}Bh]}{2Bh}$

simplify

$ratio=\frac{1}{3}$