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

1. πh²

2. $\dfrac{3}{2}$ πh²

3. $\dfrac{4}{3}$ πh²

4. 2 πh²

Let radius of cylinder be r cm.

Given, diameter = height = h cm

Radius = $\dfrac{\text{diameter}}{2} = \dfrac{\text{h}}{2}$

Total surface area of cylinder = 2πr(r + h)

$= 2 π \dfrac{\text{h}}{2} \Big(\dfrac{\text{h}}{2} + \text{h}\Big) \\[1em] = π \text{h} \times \Big(\dfrac{\text{h} + 2 \text{h}}{2}\Big) \\[1em] = π \text{h} \times \dfrac{3\text{h}}{2} \\[1em] = \dfrac{3}{2} π \text{h}^2$

Hence, option 2 is the correct option.