Question

Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.

Answer 1

Given, diameter of spherical marble = 1.4 cm

∴ Radius = `1.4/2` = 0.7 cm.

Volume of one ball = `4/3pir^3`

= `4/3pi (0.7)^3 cm^3`  ...(i) 

Diameter of beaker = 7 cm 

∴ Radius = `7/2` cm, 

Height of water (h) = 5.6 cm

∴ Volume of water = πr²h

= `pi (7/2 xx 7/2 xx 5.6) cm^3`

∴ Required No of balls dropped

= `(pi xx 49 xx 56 xx 3)/(4 xx 10 xx 4pi xx (0.7)^3)` 

= `(49 xx 56 xx 3 xx 10 xx 10 xx 10)/(4 xx 10 xx 7 xx 7 xx 7 xx 4)` 

= 150