A cylindrical vessel 60 cm in diameter is partially filled with water. A sphere, 60 cm in diameter is gently dropped into the vessel. To what further height will water rise in the cylinder? Pleasea! Explain with diagram.

Dear Student,

Please find below the solution to the asked query:

Given : A cylindrical vessel 60 cm in diameter , So

Radius of   cylindrical vessel = 30 cm

And

A sphere  60 cm in diameter , So

Radius of sphere  =  30 cm

Here ,

Volume of sphere =  Volume of water rise

Let level of water rise = h m 

So,

$$\begin{gathered} \frac{ 4 \mathrm{\pi } r^3}{3} = \mathrm{\pi } r^{2}h \\ \Rightarrow \frac{ 4 \times \mathrm{\pi } \times {30}^3}{3} = \mathrm{\pi } \times {30}^2 \times h \\ \Rightarrow \frac{ 4 \times 30}{3} = h \\ \Rightarrow h = 4 \times 10 \\ \mathbf{\Rightarrow }\mathit{h}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{40} \end{gathered}$$
Therefore,

Level of water rise = 40 cm                                                       ( Ans )


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