Question

Choose the correct answer of the following question:

If the radius of a sphere becomes 3 times, then its volume will become

(a) 3 times (b) 6 times (c) 9 times (d) 27 times [CBSE 2011]

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{sphere}\mathrm{and}\mathrm{that}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{sphere}\mathrm{be}r\mathrm{and}R,\mathrm{respectively}; \\ \mathrm{Also},\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{sphere}\mathrm{and}\mathrm{that}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{sphere}\mathrm{be}v\mathrm{and}V,\mathrm{respectively}. \\ \mathrm{We}\mathrm{have}, \\ R=3r.....\left(\mathrm{i}\right) \\ \mathrm{Now}, \\ \frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{sphere}}{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{sphere}}=\frac{\left({\displaystyle \frac{4}{3}}{\mathrm{\pi R}}^3\right)}{\left({\displaystyle \frac{4}{3}}{\mathrm{\pi r}}^3\right)} \\ ={\left(\frac{R}{r}\right)}^3 \\ ={\left(\frac{3r}{r}\right)}^3\left[\mathrm{Using}\left(\mathrm{i}\right)\right] \\ =3^3 \\ =27 \end{gathered}$$

Hence, the correct answer is option (d).