a cylinder of volume V is to be cut from a solid sphere, of radius R
show that the maximum value of V is /[4piR^3/3sqrt{3}]/

Question

a cylinder of volume V is to be cut from a solid sphere, of radius R 
show that the maximum value of V is /[4piR^3/3sqrt{3}]/

anonymous · Answer

$$4piR^3/3\sqrt{3}$$

anonymous · Answer

did you try to express h (formula for V of cylinder) in a terms of r (cylinder) & R(radius of Sphere)?
Take a V' and = 0

anonymous · Answer

take a derivative of:
V=2pi*r^2(R^2-r^2)^1/2 (r is variable)
maximize with regards to R

anonymous · Answer

find a formula for the vol of the cylinder in terms of r and h
using the relation R^2 = r^2 + (h/2)^2
where r and h are radius of cylinder base and its height.
Differentiate this formula for V wrt  h and and equate to 0 to find h corresponding to maxm volume.
then substitute for h and r  in v= pir^2h
This will give the required formula.

anonymous · Answer

jimmyrep is right - it easier to use present r(radius of cylinder) as:
r^2=R^2-(h/2)^2
put in formula for cylinder & take a derivative.
V=pi*h*(R^2-h^2/4)