Question

Choose the correct answer of the following question:

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises by

(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm [CBSE 2011]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{sphere},r=\frac{18}{2}=9\mathrm{cm}\mathrm{and} \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{vessel},R=\frac{36}{2}=18\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{rise}\mathrm{of}\mathrm{water}\mathrm{level}\mathrm{be}H. \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{water}\mathrm{rised}=\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{sphere} \\ \Rightarrow \mathrm{\pi }{R}^{2}H=\frac{4}{3}\mathrm{\pi }{r}^3 \\ \Rightarrow H=\frac{4r^3}{3R^2} \\ \Rightarrow H=\frac{4\times 9\times 9\times 9}{3\times 18\times 18} \\ \therefore H=3\mathrm{cm} \end{gathered}$$

Hence, the correct answer is option (a).