Question

Water filled in a right cylindrical tank with radius 14cm ,such that water level is 3cm below the top. when an iron ball is dropped in the tank,3003cm cube of water flows out.find the radius of the ball​

Answer 1

The radius of the ball is 10.5 cm.

Step-by-step explanation:

Given, water filled in right cylindrical tank with radius 14 cm , such that water level is 3 cm below the top.

Therefore the volume of empty portion of the tank

$=\pi r^2h$

$=\pi \times 14^2\times 3$ cm³

=1848 cm³

When an iron ball is dropped in the tank 3003 cm³of water flow out.

Therefore the total volume the iron ball is=(1848+3003)cm³

                                                                     =4851 cm³

Let the radius of the ball be = x

According to the problem,

$\frac{4}{3} \pi r^3=4851$

$\Rightarrow r^3=\frac{4852 \times 3}{4 \times \pi}$

$\Rightarrow r^3=\frac{9261}{8}$

$\Rightarrow r=\frac{21}{2}$

⇒r = 10.5

The radius of the ball is 10.5 cm.