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

• `2pi"h"^2`

• `3/2 pi"h"^2`

• `4/3 pi"h"^2`

• `pi"h"^2`

Answer 1

If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is `bb(3/2 pih^2)`.

Explanation:

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

It is given that:

`2"r" = "h" ⇒ "r" = "h"/2`

Therefore, total surface area S is:

`"S"=2pi "r"^2 + 2 pi "rh"`

`⇒ "S" = 2pi "r" ("r" +"h")`

`⇒ "S" = 2pi xx "h"/2 ("h"/2 +"h")`

`⇒ "S" = (3pi"h"^2)/2`