Question

A square pyramid has a height of 6 units and a volume of 70 units3. If a square prism has the same base area and volume as the square pyramid, what is its height?

Answer 1

Answer:

The height of the prism is $h=2\ units$

Step-by-step explanation:

step 1

Find the area of the base of the pyramid

The volume of the pyramid is equal to

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

where

B is the area of the base of pyramid

h is the height of the pyramid

we have

$V=70\ units^{3}$

$h=6\ units^{3}$

substitute and solve for B

$70=\frac{1}{3}B(6)$

$70=2B$

$B=35\ units^{2}$

step 2

Find the height of the prism

The volume of the prism is equal to

$V=Bh$

where

B is the area of the base of prism

h is the height of the prism

we have

$V=70\ units^{3}$

$B=35\ units^{2}$

substitute and solve for h

$70=35h$

$h=2\ units$