Question

In a cylindrical vessel of radius 10cm , containing some water, 9000 small spherical balls are dropped which are completely immersed in water which raises the water level . if each spherical ball is of radius 0.5 cm then find the rise in level of water in the vessel

Answer 1

Answer: Hope it helps!

Step-by-step explanation:

Answer 2

$h=1.67\times 10^{-3}\ cm$

Step-by-step explanation:

Given:

• radius of the cylindrical vessel, $R=10\ cm$

• no. of spherical balls in the vessel, $n=9000$

• radius of the ball, $r=0.5\ cm$

The rise in water level will be equal to the volume of the water displaced due to the occupancy of volume of the immersed balls.

Rise in volume:

$\Delta V=\frac{4}{3} \times \pi.r^3\times n$

$\Delta V=\frac{4}{3} \times \pi\times 0.5^3\times 9000$

$\Delta V=1500\pi\ cm^3$

Now the rise in the water height:

$\Delta V=\pi.R^2.h$

where:

$h=$ height risen

$1500\pi=\pi\times 10^2\times h$

$h=15\ cm$

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TOPIC: volume of cylinder

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