A cylindrical containet with base is to hold 64inch^3. find the dimension so that the surface area of meatal required is minimum when the container is open or close?
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This is a trivial question; but I just want to make sure:
A closed cylindrical container has a capacity of 128πm3. Determine the minimum surface area. The answer is 96π.
Volume of Cylinder, V=πr2h=128π (eq1)
Surface Area of Cylinder, SA=2π(r2+rh) (eq2)
Substitute eq(1) and eq(2); solve for the derivative of zero:
ddr(r2+128/r)=0,
solve for r.
We get r=4.
Put back into V formula, h=2.54647
Calculate Surface area: 52π
Is it possible answer is wrong? I double checked with wolfram Alpha and all my derivatives are valid
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