Question

the volume of a cylinder equal v cubic cm, where v is a constant. Find the condition that minimise the total surface area of the cylinder​

Answer 1

Answer:

volume=πr^2h. given volume=v,v=πr^2h therefore h=v/πr^2, surface area of cylinder=2πrh+2πr^2.

Step-by-step explanation:

surface area=A

A=2πrh+2πr^2.

A=2πr(v/πr^2)+2πr^2

dA/Dr=-2v/r^2+4πr

d^2/dr^2=4v/r^3+4π>0

surface area is minimum

dA/Dr=-2v/r^2+4πr=0

v=2πr^3 this the condition that minimise the total surface area of the cylinder