Question

What is the volume of a square pyramid with base edges 24 feet and slant height 37

Answer 1

Answer: The volume of pyramid is 6720 ft³

Step-by-step explanation:

Given: Base edge of a square pyramid = 24 feet

Slant height = 37 feet

Therefore height of pyramid is given by

$h^2=l^2-\dfrac{1}{2} b^2$ where h is height, l is slant height and b is base edge of pyramid

So we have

$h^2= 37^2-(\dfrac{1}{2} \times 24)^2= 37^2-12^2=1225 \\\\\Rightarrow h= \sqrt{1225} =35$

Height of pyramid is 35 feet

Now the volume of a pyramid is given by

$V=b^2\dfrac{h}{3}$ where V is volume , b is base edge and h is height of pyramid

Therefore

$V= (24)^2\dfrac{35}{3} = 6720$

Hence , the volume of pyramid is 6720 ft³