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 

\[= \pi R^2 H - \frac{4}{3}\pi r^3 \]
\[ = \pi \left( 7 \right)^2 \times 30 - \frac{4}{3}\pi \times \left( 1 \right)^3 \]
\[ = 1470\pi - 1 . 33\pi\]
\[ = 1468 . 67\pi {cm}^3\]

Thus, the volume of the water is 1468.67π cm³ .