Question

87. If the height of a cone is doubled, then find
the percentage increase in its volume.​

Answer 1

Step-by-step explanation:

In 1st case:-

Base radius = r

Height = h

therefore, volume will be,

$x = \frac{\pi {r}^{2} h}{3}$

In 2nd case:-

Base radius = r

Height = 2h

therefore, it's volume will be

$y = \frac{\pi {r}^{2}2h }{3}$

$= \frac{2\pi {r}^{2} h}{3}$

therefore increased in volume,

$= \frac{y - x}{x} \times 100 \: percent$

$= \frac{ \frac{2\pi {r}^{2}h }{3} - \frac{\pi {r}^{2} h}{3} }{ \frac{\pi {r}^{2}h }{3} } \times 100 \: percent$

$= \frac{ \frac{2\pi {r}^{2} h - \pi {r}^{2} h}{3} }{ \frac{\pi {r}^{2}h }{3} } \times 100 \: percent$

$= \frac{ \frac{\pi {r}^{2}h }{3} }{ \frac{\pi {r}^{2} h}{3} } \times 100 \: percent$

$= 1 \times 100 \: percent$

$= 100 \: percent$

Answe:- The volume will be increased by 100%.