Question

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water . Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm .

Answer 1

Diameter of the marbles = 1.4 cm
Radius of the marbles, r = \[\frac{1 . 4}{2} = 0 . 7 cm\]

Diameter of the cylinderical beaker = 7 cm
Radius of the beaker = \[\frac{7}{2} = 3 . 5 cm\]

Rise in the level of water = 5.6 cm
let the number of marbles be n.

\[n \times \text { volume of the marbles = volume of the water risen }\]

\[ \Rightarrow n = \frac{\text { volume of the water risen }}{\text { volume of the marbles }}\]

\[ \Rightarrow n = \frac{\pi \left( \frac{7}{2} \right)^2 \left( 5 . 6 \right)}{\frac{4}{3}\pi \left( 0 . 7 \right)^3} = 150\]

Hence, the number marbles will be 150.