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

Answer

2.5 cm

Explanation

`(4)/(3) pi xx 3 xx 3 xx 3 = (4)/(3) pi xx (3)/(2) xx (3)/(2) xx (3)/(2) + (4)/(3) pi xx 2 xx 2 xx 2 + (4)/(3) pir^(3)`
`rArr (27)/(8) + 8 + r^(3) = 27 rArr r^(3) = (27 - (91)/(8)) = ((216 - 91))/(8) = (125)/(8) = ((5)/(2))^(3)`
`:. r = (5)/(2) cm = 2.5 cm`