Cylinder shape in Geometry

Cylinder

A cylinder is taken to mean a finite section of a right circular cylinder with its ends closed to form two circular surfaces, as in the figure above. If the cylinder has a radius r and length (height) h, then its volume is given by

V = $πr 2 h$

and its surface area is:

Area of the top is $π r 2$

Area of the bottom is $π r 2$

Area of the side is $2π r h$

Therefore without the top or bottom, the surface area is

A = 2π r h

With the top and bottom, the surface area is

A =

2π r 2 +

2π r h =

2π r (

r

+ h)

For a given volume, the cylinder with the smallest surface area has h = 2r. For a given surface area, the cylinder with the largest volume has h = 2r, (i.e. cylinder fits in a cube (height = diameter.)