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 each marble = 1.4 cm

Radius of each marble = 0.7 cm

Volume of each marble `= 4/3pir^3 = 4/3pixx(0.7)^3 "cm"^3`

The water rises as a cylindrical column.

Volume of cylindrical column filled with water `= pir^2h =pi xx (7/2)^2 xx 5.6  "cm"^3`

Total number of marbles

`="Volume of cylindrical water column"/"Volume of marble" `

`= (pixx(7/2)^2 xx 5.6)/ (4/3pi xx (0.7)^3) `

`= (7xx7xx5.6xx3)/(2xx2xx4xx0.7xx0.7xx0.7)`

`=150`