Question

If height and radius of a cone is doubled find percentage increase in volume

Answer 1

Volume of a cone = 1/3 × πr²h


Now, the height and radius are doubled. So the volume would be

1/3 × π(2r)² × 2h

= 1/3 × π4r² × 2h

= 8/3 × πr²h

Now, net increase in the volume

= (8/3 × πr²h) - (1/3 × πr²h)

= πr²h (8/3 - 1/3)

= 7/3 × πr²h

So percentage = increase/original × 100

=
$\frac{ \frac{7}{3} \pi \: r {}^{2}h }{ \frac{1}{3}\pi {r}^{2}h } \times 100 \\ \\ = > 7 \times 100 \\ \\ = 700\%$


Answer :- 700%