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frez [133]
3 years ago
14

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 t

he side length of the square base
Mathematics
1 answer:
ella [17]3 years ago
5 0

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

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