Question

A both sides closed circular cylinder has a surface area of 400 cm2. Determine

Answer 1

The dimension of the maximum volume of the circular cylinder is

200r - πr³.

What is a cylinder?

A cylinder is a three-dimensional figure that has a radius and a height.

The volume of a cylinder is given as:

Example:

The volume of a cup with a height 5 cm and a radius 2 cm is

Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm

We have,

The surface area of the cylinder = 400 cm²

The surface area of a cylinder = 2πrh + 2πr²

400 =  2πrh + 2πr²

400 = 2πr (h + r)

400 / 2πr = h + r

h = (400/2πr) - r

The volume of the closed circular cylinder.

V = πr²h

V = π x r² x {(400/2πr) - r}

V = π x r² x (400 - 2πr²) / 2πr

V = r x (400 - 2πr²) / 2

V = r x (200 - πr²)

V = 200r - πr³

Thus,

The dimension of maximum volume is 200r - πr³.

Learn more about cylinder here:

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