In the given problem shape of the object is sphere to find answer of this question need to use sphere volume formula. Question from RS Aggarwal book chapter volume and surface area of solid, page number 810, exercise 17B, problem number 11

Deepak BoraNewbie

# 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.

Share

Given data,

Radius of sphere = 3 cm

Radius of first ball = 1.5 cm

Radius of second ball = 2 cm

To find

Radius of the third ball be r cm.

Volume of third ball = Volume of original sphere – Sum of volumes of other two balls

= ([4/3] Ï€rÂ³) – ([4/3] Ï€rÂ³ + [4/3] Ï€rÂ³)

= ([4/3] Ï€ * 3Â³) – (([4/3] Ï€ * 1.5Â³) + ([4/3] Ï€ * 2Â³))

= [125 * Ï€ ] / 6

now,

volume of third ball =

[4/3] Ï€rÂ³ = [125 * Ï€ ] / 6

[4/3] rÂ³ = [125] / 6

r = 3âˆš [ (125*3) / (4*6)]

r = 2. 5 cm

âˆ´ radius of the third ball is 2.5 cm