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

Given, diameter of a marble = 1.4 cm

∴ Radius of marble = `1.4/2` = 0.7 cm

So, volume of one marble

= `4/3 pi(0.7)^3`

= `4/3 pi xx 0.343`

= `1.372/3 pi  "cm"^3`

Also, given diameter of beaker = 7 cm

∴ Radius of beaker = `7/2` = 3.5 cm

Height of water level raised = 5.6 cm

∴ Volume of the raised water in beaker

= π(3.5)² × 5.6

= 68.6π cm³

Now, required number of marbles

= `"Volume of the raised water in beaker"/"Volume of one spherical marble"`

= `(68.6 pi)/(1.372 pi) xx 3`

= 150