Question

Find the maximum volume of a right circular cylinder if the sum of its radius and height is 6 units.

Answer 1

Let height of cylinder be h and radius be r

=>r+h=6

=>h=6-r

Volume of cylinder V =pi *r^2*h

Pi*r^2*(6-r)

Pi*(6r^2-r^3)

For maximum or minimum volume

dv/dr should be equals to zero

dv/dr =pi(12r-3r^2) =0

12r=3r*r

r=4

Put value of r in given equation

R+h=6

h=2

Volume of cylinder =pi(4)^2*(2)

Pi*(16)*(2)

32pi is maximum volume