3 years ago

Find the dimensions of a closed right circular cylindrical can of smallest surface area whose volume is 128pi cm^3

1 answer:

4 0

The surface area of a cylindrical can is equal to the sum of the area of two circles and the body of the cylinder: 2πr2 + 2πrh. volume is equal to πr2h.

V = πr2h = 128 pi
r2h = 128
h = 128/r2

A = 2πr2 + 2πrh
A = 2πr2 + 2πr*(128/r2)
A = 2πr2 + 256 π / r

the optimum dimensions is determined by taking the first derivative and equating to zero.

dA = 4 πr - 256 π /r2 = 0
r = 4 cm
h = 8 cm

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