If the height of a cone is doubled, then its volume is increased by :

1. 100%

2. 200%

3. 300%

4. 400%

For older cone,

⇒ Radius = r

⇒ Height = h

⇒ Volume = v

For new cone,

⇒ Radius = r

⇒ Height = 2h

⇒ Volume = V

Volume of cone = $\dfrac{1}{3}π \times \text{(radius)}^2 \times \text{height}$

Increase in the volume of cone = $\dfrac{\text{Volume of new cone - Volume of old cone}}{\text{Volume of old cone}} \times 100$

$= \dfrac{\text{V - v}}{\text{v}} \times 100 \\[1em] = \dfrac{(\dfrac{1}{3}π \text{r}^2 \times \text{2h}) - (\dfrac{1}{3}π \text{r}^2 \text{h})}{\dfrac{1}{3}π \text{r}^2 \text{h}} \times 100 \\[1em] = \dfrac{\dfrac{1}{3}π \text{r}^2 \text{h}(2 - 1)}{\dfrac{1}{3}π \text{r}^2 \text{h}} \times 100 \\[1em] = 100\%.$

Hence, option 1 is the correct option.