Question

the radius of sphere is 10 cm . if its radius is increased by 1 cm , then by what percent of volume of sphere increased

Answer 1

radius of the sphere, r = 10 cm
volume of the sphere = $\frac{4}{3}{\mathrm{\pi r}}^3=\frac{4}{3}\mathrm{\pi }\left(1000\right){\mathrm{cm}}^3$
new radius , R = 11 cm
new volume = $\frac{4}{3}{\mathrm{\pi R}}^3=\frac{4}{3}\mathrm{\pi }\left(1331\right){\mathrm{cm}}^3$
increase in volume = new vol. - original vol. = $\frac{4}{3}\mathrm{\pi }\left(331\right){\mathrm{cm}}^3$

$$\begin{gathered} percentincrease=\left[\frac{increaseinvol}{originalvol}\times 100\right]\% \\ =\left[\frac{{\displaystyle \frac{4}{3}}\mathrm{\pi }\left(331\right)}{{\displaystyle \frac{4}{3}}\mathrm{\pi }\left(1000\right)}\times 100\right]\%=33.1\% \end{gathered}$$