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? 2 units 4 units 6 units 8 units

Answer 1

Answer:

The height is 2 units

Step-by-step explanation:

Find the area of the base of the square pyramid

we know that

The volume of the square pyramid is equal to

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

where

B is the area of the base and H is the height of the pyramid

we have

$H=6\ units$

$V=70\ units^{3}$

substitute in the formula and solve for B

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

$B=70/2=35\ units^{2}$

step 2

Find the height of the square prism

we know that

The volume of the square prism is equal to

$V=Bh$

where

B is the area of the base and h is the height of the prism

we have

$B=35\ units^{2}$

$V=70\ units^{3}$

substitute in the formula and solve for h

$70=(35)h$

$h=2\ units$