A cylindrical jar having a base of radius 15 cm, is filled with water up to a height of 20 cm. If a solid iron spherical ball of radius 10 cm is dropped in the jar to submerge completely in the water, then the increase in the level of water is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(5\frac{25}{27}\) cm
A solid ball that sinks completely pushes up water equal to its own volume. The raised water forms a cylinder of the jar’s radius, so the rise in level is the volume of the ball divided by the area of the base. The 20 cm of water already in the jar does not enter the working.
Volume of the ball \(\displaystyle =\frac{4}{3}\pi\times10^3=\frac{4000}{3}\pi\,\mathrm{cm^3}\)
Area of the base of the jar \(=\pi\times15^2=225\pi\,\mathrm{cm^2}\)
Rise in level \(\displaystyle =\frac{4000\pi}{3\times225\pi}=\frac{4000}{675}=\frac{160}{27}=5\frac{25}{27}\,\mathrm{cm}\)