Marbles of diameter 1.4 cm are dropped

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.

Solution:

Given, diameter of a marble = 1.4 cm

$\therefore \quad$ Radius of marble $=\frac{1.4}{2}=0.7 \mathrm{~cm}$

So, $\quad$ volume of one marble $=\frac{4}{3} \pi(0.7)^{3}$

$=\frac{4}{3} \pi \times 0.343=\frac{1.372}{3} \pi \mathrm{cm}^{3}$

Also, given diameter of beaker = 7 cm

$\therefore$ Radius of beaker $=\frac{7}{2}=3.5 \mathrm{~cm}$

Height of water level raised $=5.6 \mathrm{~cm}$

 

$\therefore$ Volume of the raised water in beaker $=\pi(3.5)^{2} \times 5.6=68.6 \pi \mathrm{cm}^{3}$

Now, required number of marbles $=\frac{\text { Volume of the raised water in beaker }}{\text { Volume of one spherical marble }}$

$=\frac{68.6 \pi}{1.372 \pi} \times 3=150$

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