Question

On decreasing the radius of a sphere by 20% .by what % its volume decrease

Answer 1

$let \: \: r \: \: be \: \: the \: \: radius \\ initial \: \: volume = \frac{4}{3} \pi {r}^{3 } \\ \\ after \: \: decreasing \: \: radius = 0.8r \\ new \: \: volume = \frac{4}{3} \pi {(0.8r)}^{3 } \\ \\ \%decrease \: \: in \: \: volume \\ = \frac{initial \: volume -new \: volume }{initial \: volume} \times 100 \\ = (1 - {(0.8)}^{3} ) \times 100 = 48.8\%$