(Q12).Spherical marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm, which contains some water. Find the number of marbles that should be dropped into the beaker, so that water level rises by 5.6 cm.

Rise in the water level is seen in cylindrical shape of Radius = Beaker radius

=
d
2
 =
= cm
image

Height ‘h’ of the rise = cm.

∴ Volume of the ‘water rise’ = πr2h

=
× × ×
=
××

=

Volume of each marble dropped =
4
3
 πr3
Where radius r =
d
2
 =
= cm
∴ V =
×
× × ×

= cm3

∴ Volume of the ‘rise’ = Total volume of the marbles.

Let the number of marbles be ‘n’ then n × volume of each marble = volume of the rise.

n × =

=

∴ Number of marbles = .