Question

The radius of a solid cylinder is doubled keeping the height same. The percentage increase in its volume is:

विकल्प

• 200%

• 100%

• 400%

• 300%

Answer 1

300%

Explanation:

Before change:

Radius of cylinder = r

Height of cylinder = h

Volume of cylinder = πr²h

After change:

Radius of cylinder = 2r

Height of cylinder = h

Volume of cylinder = π(2r)²h = 4πr²h

Difference in volume = Volume after change − Volume before change
= 4πr²h − πr²h

= 3πr²h

Percentage increase in volume

\[{} = \frac{\text{Difference in vol.}}{\text{Vol. of cylinder before change}} \times 100\]

\[{} = \frac{3\pi r^2 h}{\pi r^2 h} \times 100\]

= 3 × 100

=300