Question

A sculpture is in the shape of a square pyramid. The sculpture has a height of 36 feet and a volume of 19,200 cubic feet. Find the side length of the square base

Answer 1

Answer:

40ft

Step-by-step explanation:

The volume of a square pyramid is given by:

$V=\frac{l^2h}{3}$

where V is the volume, l is the length of the square base, and h is the height.

Since we need to find the length, we solve for $l$ in the last equation:

$l^2h=3V\\\\l^2=\frac{3V}{h} \\\\l=\sqrt{\frac{3V}{h} }$

and now, we substitute the known values:

$V=19,200ft^3\\h=36ft$

and we get the following:

$l=\sqrt{\frac{3(19,200ft^3)}{36ft} }\\ \\l=40ft$

the length of the square base is 40ft