Question

(iii) Water is filled in a right cylindrical tank with base radius 14 cm, such that water
level is 3 cm below the top. When an iron ball is dropped in the tank, 3003 cm3 of
water flows out. Find the radius of the ball.​

Answer 1

Answer:

r=10.03529197 cm

Step-by-step explanation:

The volume of the ball is the volume of water displaced when the iron ball is dropped in the tank.

Volume of water displaced consists of volume of water that overflowed and the volume of water that occupied the 3 cm from the top

That is;

volume of water that occupied the 3 cm from the top of the cylinder is

$V_1=\pi *r^2*h\\V_1=\frac{22}{7}*14^2*2\\ \\V_1=1232 cm^3$

volume of water that overflowed is

$V_2= 3003cm^3$

therefore

$V= V_1+V_2\\V= 1232+3003\\V= 4235cm^3$

The volume of a sphere is given as;

$V=\frac{4}{3}*\pi  *r^3\\4235=\frac{4}{3} *\frac{22}{7} *r^3\\\\r^3=1010.625\\\\r=\sqrt[3]{101.625} \\\\r=10.03529197 cm$