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A pyramid with a square base has a volume of 320 and a height of 15. What is the perimeter of the base?

Answer 1

Savannah Aguilar

The perimeter of the base is #32#.

The following is the formula for a right rectangular pyramid's volume:

#V=(l*w*h)/3#, where #V=#Volume, #l=#length, #w=#width, and #h=#height.

Since the base is square, #l=w# so we can represent #l*w# as #l^2#

#V=(l^2*h)/3#

Using the previously provided values, we write:

#320=(l^2*15)/3#

#320=(l^2*5cancel15)/(1cancel3)#

Divide both sides by #5#.

#320/5=(l^2*5)/5#

#64=(l^2*1cancel5)/(1cancel5)#

#64=l^2#

Remembering that the answer must be a positive integer, find the square root of each side.

#8=l#

Since the length of the side of the base is #8#, and the base is a square, the perimeter will be:

#P=4l#

#P=4xx8#

#P=32#

The perimeter of the base is #32#.

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Answer from HIX Tutor

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