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#### 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.

Solution

Given:- Diameter of marble = 1.4 cm

Diameter of beaker = 7cm

Diameter of marble = 1.4 cm

$\text{ Radius of marble}=\frac{1.4}{2}=0.7 cm$

The volume of 1 marble

$=\frac{4}{3} \pi r^3=\frac{4}{3}\pi (0.7)^3$

$=\frac{4}{3} \times 3.14 \times 0.343=1.43cm^3$

Diameter of beaker = 7 cm

$\text{ Radius of beaker}=\frac{7}{2}=3.5 cm$

Water level rises(h) = 5.6cm

Volume of water

$=\pi r^2 h=(3.14)(3.5)^2(5.6)$

$=215.40$

$\text{ Number of marbles required}=\frac{\text {volume of water }}{\text {volume of 1 marble }}$

$=\frac{215.40}{1.43}=150$

Hence 150 marbles should be dropped into the beaker.

So that the water level rises by 5.6 cm.