A cylindrical glass of diameter 14 cm contains water up to a height of 30 cm. A metal sphere of diameter 2 cm is immersed in it. Find the volume of the water.

Answer: Volume of water = \(1468\tfrac23\pi\) cm³ ≈ 1468.67π cm³ (about 4615.8 cm³ with π = 22/7)

Radius of glass \(R=7\) cm; level of water with the sphere inside = 30 cm. Radius of sphere \(r=1\) cm.

Volume up to 30 cm \(=\pi R^2h=\pi\times49\times30=1470\pi\)

Volume of sphere \(=\tfrac43\pi r^3=\tfrac43\pi\)

The sphere occupies part of the 30 cm column, so

\[\text{water}=1470\pi-\tfrac43\pi=\tfrac{4406}{3}\pi\]

\[\approx1468.67\pi\ \text{cm}^3\approx4615.81\ \text{cm}^3\]