Question

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.

Answer 1

Radius of sphere = 3 cm

Radius of first ball = 1.5 cm

Radius of second ball = 2 cm 

Radius of second ball = 2 cm

`=4/3pixx3^3 -(4/3pixx3^3/2+4/3pixx2^3)`

`=4/3pixx3xx3xx3 - (4/3pixx3/2xx3/2xx3/2+4/3pixx2xx2xx2)`

`=4pixx3xx3-(pixx(3xx3)/2 + 4/3pixx2xx2xx2)`

`=36pi - (pi9/2+32/3pi)`

`=((36xx6-9xx3-32xx2)/6)pi `

`=((216-27-64)/6)pi =(125pi)/6`

Therefore,

`4/3pir^3 = (125pi)/6`

`Or, r = root(3)((125xx3)/(4xx6)) = root(3)(125/8) = 5/2 = 2.5  "cm"`