Question

the height and diameter of a cylinder are 14cm. the cylinder is filled with water upto the brim. four equal solid spheres are placed into it. the diameter of each sphere is equal to the radius of the bade of the cylinder. what fraction of water overflows?

Answer 1

3/4 of the water overflows

Answer 2

Diameter & height of cylinder are equal

Let diameter of cylinder = x

Then, height of cylinder also = x

Radius of cylinder = x/2

Radius of 4 ball = x/4

According to Question;

Volume of cylinder - 4(Volume of each ball)

πr²h - 4(4/3πr³)

π(x/2)² x - 16/3 π (x/4)³

π [(x³/4) - 16/3 (x³/64)

π (x³/4 - x³/12)

22/7 × x³/6

0.524 x³

Percentage of water that flows

0.54x³/πx³/4 × 10

(0.524 × 4 × 7 × 100)/22

0.666 × 100

66.6 %