Choose the correct answer of the following question:

Question:

Choose the correct answer of the following question:

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises by

(a) 3 cm                         (b) 4 cm                         (c) 5 cm                         (d) 6 cm  

Solution:

We have,

Radius of the sphere, $r=\frac{18}{2}=9 \mathrm{~cm}$ and

Radius of the cylindrical vessel, $R=\frac{36}{2}=18 \mathrm{~cm}$

Let the rise of water level be $H$.

Now,

Volume of the water rised $=$ Volume of the sphere

$\Rightarrow \pi R^{2} H=\frac{4}{3} \pi r^{3}$

$\Rightarrow H=\frac{4 r^{3}}{3 R^{2}}$

$\Rightarrow H=\frac{4 \times 9 \times 9 \times 9}{3 \times 18 \times 18}$

$\therefore H=3 \mathrm{~cm}$

Hence, the correct answer is option (a).

 

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