Question #279187

A tent of a given volume has a square base of side 2a, has its four sides vertical of height b and is surmounted by a regular pyramid of height 1. find the values of a and b in terms of height I such that the canvas required for its construction is minimum.

1
Expert's answer
2021-12-14T18:33:26-0500

area of canvas:

S=4ah2+a22ahS=4a\sqrt{h^2+a^2}-2ah


Sh=4ha2a2h2+a42a=0S'_h=\frac{4ha^2}{\sqrt{a^2h^2+a^4}}-2a=0


4h2=h2+a24h^2=h^2+a^2

a=h3a=h\sqrt 3


b2=a2+h2=4h2b^2=a^2+h^2=4h^2

b=2hb=2h


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