Height and radius of cylinder with the least possible surface area given the volume

A cylinder has a volume of 100 cubic inches. What is the height and radius of such a cylinder with the least possible surface area?

Constant volume of a cylinder = (pi)r^(2)h

Surface area, including both ends = 2(pi)r^2 + 2(pi)rh

Re: Height and radius of cylinder with the least possible surface area given the volu

Therefore now minimise surface area in terms of height.

Re: Height and radius of cylinder with the least possible surface area given the volu

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**Roleparadise** A cylinder has a volume of 100 cubic inches. What is the height and radius of such a cylinder with the least possible surface area?

Constant volume of a cylinder = (pi)r^(2)h

Surface area, including both ends = 2(pi)r^2 + 2(pi)rh

(pi)r^2h=100 So h=100/(pi)r^2 Sub this into S getting S=2(pi)r^2+200/r Put derivative=0 to find required r and then h

Re: Height and radius of cylinder with the least possible surface area given the volu

You can let and substitute into your surface area function and differentiate with respect to r.

Or, if you know how to use Lagrange multipliers, you can use them: there exists a constant such that

, where A(r,h) and V(r,h) are the surface area and volume functions, respectively.