Question

If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is

Options

• \[2 \pi h^2\]

   

• \[\frac{3}{2} \pi h^2\]

• \[\frac{4}{3} \pi h^2\]

   

• \[\pi h^2\]

Answer 1

Let r be the radius of the cylinder and h be its height.

It is given that:

`2r = h ⇒ r = h/2`

Therefore, total surface area S is:

`S=2pi r^2 + 2 pi r h`

`⇒ S = 2pi r ( r +h)`

`⇒ S = 2pi xx h/2 (h/2 +h)`

`⇒ S = (3pih^2)/2`