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A frustum of pyramid consists of square base of length 10 cm and a top square of 7 cm.
The heights of the frustum is 6 cm calculate
(A) the surface area
(B) volume
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Volume
See this Wikipedia article or this WEB-page.
The volume formula of a frustum of a square pyramid was introduced by the ancient Egyptian mathematics
in what is called the Moscow Mathematical Papyrus, written ca. 1850 BC.:
V =
where a and b are the base and top side lengths of the truncated pyramid, and h is the height.
The Egyptians knew the correct formula for obtaining the volume of a truncated square pyramid,
but no proof of this equation is given in the Moscow papyrus.
By applying the formula, we get V = = 438 .
By the way, the proof is easy.
As you know, the volume of the larger pyramid is = , where is its height.
The volume of the smaller pyramid is = , where is its height.
Obviously, from similarity = and = , where const is a constant value independent of "a" and "b".
Then = , = .
The volume of the frustum is the difference
V = = = = .
But const*(a-b) = = h, the height of the frustum.
Therefore, the volume of the frustum is V = . QED.