Question

A hemispherical bowl of radius 3 cm contains water to the rim. When marbles each of radius 5 mm are dropped into the bowl, one third of water flows out. Find the number of marbles dropped into the bowl.

Answer 1

let the radius of hemisphere be d and marbles be r and n be the no. of marbles.
total volume of marbles dropped into the bowl= volume of water displaced.
i.e.
$\frac{4}{3} \pi {r}^{3}n = \frac{1}{3} \ \frac{2}{3} \pi \ {d}^{3 } \\ \\ \frac{1}{3} ( {3}^{3}) = ({ \frac{5}{10} })^{3} n \\ \\ n = 9(8) \\ n = 72$
n=72