A solid is formed by attaching a hemisphere to each end of a cylinder. If the total volume is to be 120cm^3, find the radius (in cm) of the cylinder that produces the minimum surface area. Express your answer correct to 2 decimal places. Help!?
1 Answer
Explanation:
Assume without loss of generality the cylinder has length
Two hemispheres attached to either end have the equivalent volume of a single sphere,
Then we write,
The surface area of the geometric object will be the surface area of a sphere with radius
So we write,
Substituting the definition of
Given that
We solve for the turning points by differentiating and equating with zero to find the value(s) of
Setting