Question

a cylindrical vessel of diameter 21 cm contains water upto a certain level .50 balls of radius 2.1 cm are dropped into the vessel.find the rise in the level of water

Answer 1

Answer: 0.14773 cm

Step-by-step explanation:

Here the diameter of the cylinder = 21 cm

⇒ The radius of the cylinder = $\frac{21}{2}= 10.5\text{ cm}$

Let rise in the vessel after filling it by the 50 balls = h cm

Thus, the volume of the cylindrical vessel having the rise h cm

= $\pi (10.5)^2 h$

= $110.25 \pi h$

Also, the radius of one ball = 2.1 cm

$\text{the total volume of a ball} =\frac{3}{4}\pi(2.1)^2=\frac{13.23}{4}\pi$

$\text{the total volume of 50 balls} =50\times \frac{13.23}{4}\pi$

$=\frac{65.15}{4}\pi$

For filling the vessel,

$110.25 \pi h=\frac{65.15}{4}\pi$

$110.25 h = \frac{65.15}{4}$

$h=\frac{65.15}{441}$

$h=0.147732426\approx 0.14773\text{ cm}$