Question

As shown in the figure, a cylindrical glass contains water. A metal sphere of diameter 2 cm is immersed in it. Find the volume of the water .

Answer 1

Radius of the metallic sphere, r = $\frac{2}{2}$ = 1 cm

Radius of the cylindrical glass, R = $\frac{14}{2}$ = 7 cm

Height of water in cylindrical glass, H = 30 cm

∴ Volume of the water = Volume of water in the cylindrical glass − Volume of the metallic sphere
$$\begin{gathered} =\mathrm{\pi }{R}^{2}H-\frac{4}{3}\mathrm{\pi }{r}^3 \\ =\mathrm{\pi }{\left(7\right)}^2\times 30-\frac{4}{3}\mathrm{\pi }\times {\left(1\right)}^3 \\ =1470\mathrm{\pi }-1.33\mathrm{\pi } \\ =1468.67\mathrm{\pi }{\mathrm{cm}}^3 \end{gathered}$$
Thus, the volume of the water is 1468.67$\mathrm{\pi }$ cm³.