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
[tex]h^2=l^2-\dfrac{1}{2} b^2[/tex] where h is height, l is slant height and b is base edge of pyramid
So we have
[tex]h^2= 37^2-(\dfrac{1}{2} \times 24)^2= 37^2-12^2=1225 \\\\\Rightarrow h= \sqrt{1225} =35[/tex]
Height of pyramid is 35 feet
Now the volume of a pyramid is given by
[tex]V=b^2\dfrac{h}{3}[/tex] where V is volume , b is base edge and h is height of pyramid
Therefore
[tex]V= (24)^2\dfrac{35}{3} = 6720[/tex]
Hence , the volume of pyramid is 6720 ft³
