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
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
You can let $\displaystyle h = \frac{100}{\pi r^2}$ and substitute $\displaystyle h$ 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 $\displaystyle \lambda$ such that
$\displaystyle \nabla A = \lambda \nabla V$, where A(r,h) and V(r,h) are the surface area and volume functions, respectively.