Question

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

Answer 1

Solution:

Volume of water in the vessel = Volume of the inverted cone $=\frac{1}{3} \times \pi \times(5)^{2} \times 8 \mathrm{~cm}^{3}$

Let the number of lead shots $= n$

Volume of one lead shot $=\frac{4}{3} \times \pi \times(0.5)^{3}$

$\therefore$  Total volume of lead shots = Volume of water flowing out

 $\Rightarrow n \times$ $\frac{4}{3} \times \pi \times(0.5)^{3}=\frac{1}{4} \times \frac{1}{3} \times \pi \times(5)^{2} \times 8$

$\begin{aligned} &\Rightarrow \mathrm{n}=\frac{25 \times 8}{16 \times 0.125} \\ &\Rightarrow n=100 \end{aligned}$