Question:   Two balls, one 2 inch radius and the other 3 inch radius, are placed in a cylindrical jar 9 inch in diameter, as shown in Figure. Find the  volume of water necessary to cover them?

Solution

Given: Diameter of the cylinder=9 inch

Height of the cylinder =?

Radius of the sphere(the two balls) r1=2 inch & r2=3 inch

Height of water in the cylinder H=?

By Pythagoras Theorem , length of Hypo= sum of the squares of the two legs

Volume of Water required

to cover two unequal balls       = Volume of cylinder – Volume of two balls

         = π r²h-  4/3 π ( r1³ + r2³)

  = π (r²h – 4/3 r³)

    = π (9/2 × 9/2 × 8 ) – (4/3 × (3 ×3 ×3 + 2 × 2 ×2))

  = π ( 162 – ( 4/3 × (27 + 8))

  = π ( 162 – 46.66)

  = π (115.34)

    = 362.16 cubic inches.

The volume of water required to cover both balls is 362.16 cu.inches