Q. 193.7( 3 Votes )

# 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 :

**Given:** Diameter of marble = 1.4 cm

Diameter of cylindrical beaker = 7 cm

Height of water level = 5.6 cm

**Formula used:**

The volume of sphere =

Volume of cylinder = πr^{2}h

**Explanation:**

diameter of a marbles = 1.4 cm

∴ Radius of marble = = 0.7 cm

So, volume of one marble =

Also, given diameter of beaker = 7 cm

∴ Radius of beaker = = 3.5 cm

Height of water level raised = 5.6 cm

∴ Volume of the raised water in beaker = π r^{2} h

= π (3.5)^{2} × 5.6

= 68.6 π

Let n marbles be dropped into the beaker,

Hence n × volume of marble = volume of water raised

⇒

⇒

⇒ n = 150

Hence the number of marbles required are 150.

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