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.

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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

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] πr³) – ([4/3] πr³ + [4/3] πr³)

= ([4/3] π * 3³) – (([4/3] π * 1.5³) + ([4/3] π * 2³))

= [125 * π ] / 6

now,

volume of third ball =

[4/3] πr³ = [125 * π ] / 6

[4/3] r³ = [125] / 6

r = 3√ [ (125*3) / (4*6)]

r = 2. 5 cm

∴ radius of the third ball is 2.5 cm