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

Question

asked Jan 2, 2021 127k views

1 Answer

Michael Cohen · Answer 1 · 2021-01-06T22:32:13+0000

Answer:

40ft

Explanation:

The volume of a square pyramid is given by:

V=(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
in the last equation:

$l^2h=3V\\\\l^2=(3V)/(h) \\\\l=\sqrt{(3V)/(h) }$

and now, we substitute the known values:

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

and we get the following:

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

the length of the square base is 40ft