Volume , surface area of a cylinder?

Question

A chemical factory wishes to make a cylindrical container, of thin metal to hold 10 cm^3, using the least possible area of metal. If the outside surface is S cm^2, and the radius is R cm , show that S=2pieR^2 + 20/r and hence find the required radius and height for the container ( leave pie in the answer)

Como · Answer

S = 2πr² + 2πrh

V = πr²h
10 = πr²h
h = 10 / πr²

S = 2πr² + 2πr (10/πr²)
S = 2πr² + 20 / r

S ` (r) = 4π r - 20 / r² = 0
4π r = 20 / r²
4π r³ = 20 
π r³ = 5
r = 1.71 /π  cm

h = 10 / (πr²) = 10 / (π x 1.17²) = 7.31 / π cm

Volume , surface area of a cylinder?

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