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A vendor is using an 8-ft by 8-ft tent for a craft fair. The legs of the tent are 9 ft tall and the top forms a square pyramid with a height of 3 ft. What is the volume, in cubic feet, of space the tent occupies?
JMAP geometry math pyramis prism
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A vendor is using an 8-ft by 8-ft tent for a craft fair. The legs of the tent are 9 ft tall and the top forms a square pyramid with a height of 3 ft.

What is the volume, in cubic feet, of space the tent occupies?

1) 256

2) 640

3) 672

4) 768

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peter
Asked by peterrep:911
University of Lagos Nigeria
23 June 2020

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1 answer(s)

judziy
Judziy answeredrep:880
University of Benin Nigeria
23 June 2020
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The diagram above comprises of a square base pyramid (at the top) and a square base prims (below).

Thus, the total volume = Volume of pyramid + Volume of prism

Volume of pyramid = 1/3 x Ah

Where A and h are the base area and height of the pyramid respectively.

Since the base is a square, A = Length x Width

A = 8 x 8 = 64

Therefore, Volume of pyramid = 1/3 x 64 x 3

= 64

Volume of prims = L x W x H

Where L, W and H are the Length, Width and Hight of the square base prism respectively

Volume of prism = 8 x 8 x 9

= 576.

Thus, total volume = 64 + 576

= 640

Ans 2

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