Question

if the volume of the sphere increased by 20% find the increased percentage in the radius of the sphere.

Answer 1

Dear Student,
$$\begin{gathered} \mathrm{Let}\mathrm{initial}\mathrm{volume}\mathrm{and}\mathrm{radius}\mathrm{be}\mathrm{V}\mathrm{and}\mathrm{R}\mathrm{respectively} \\ \mathrm{V}=\frac{4}{3}{\mathrm{\pi R}}^3 \\ \mathrm{now}\mathrm{after}\mathrm{increasing}\mathrm{volume}\mathrm{by}20\%\mathrm{new}\mathrm{volume}\mathrm{will}\mathrm{be} \\ \mathrm{V}\text{'}=\mathrm{V}+\frac{20\mathrm{V}}{100}=1.2\mathrm{V} \\ \mathrm{and}\mathrm{let}\mathrm{radius}\mathrm{be}\mathrm{R}\text{'}. \\ \mathrm{V}\text{'}=\frac{4}{3}\mathrm{\pi R}{\text{'}}^3 \\ \mathrm{V}\text{'}=1.2\mathrm{V} \\ \frac{4}{3}\mathrm{\pi R}{\text{'}}^3=1.2\frac{4}{3}{\mathrm{\pi R}}^3 \\ \mathrm{R}{\text{'}}^3=1.2{\mathrm{R}}^3 \\ \mathrm{Apply}\mathrm{cube}\mathrm{root}\mathrm{on}\mathrm{both}\mathrm{side}\mathrm{we}\mathrm{get}. \\ \mathrm{R}\text{'}=1.063\mathrm{R} \\ \mathrm{Radius}\mathrm{will}\mathrm{increse}\mathrm{by}6.3\%. \end{gathered}$$
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