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# A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of the two of the balls are 2 cm and 1.5 cm respectively. Determine the diameter of the third ball?

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Please some help me with the solution.

This question is from maths class 10 rd sharma, chapter 16, exercise 16.1 ; In this question we have toh find daimeter of third ball .

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

This is very important question of mensuration for class 10 board exam.

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1. Radius of the spherical ball = 3 cm

We know that,

The volume of the sphere = 4/3 πr3

So, it’s volume (V) = 4/3 πr3

That the ball is melted and recast into 3 spherical balls.

Volume (V1) of first ball = 4/3 π 1.53

Volume (V2) of second ball = 4/3 π23

Let the radius of the third ball = r cm

Volume of third ball (V3) = 4/3 πr3

Volume of the spherical ball is equal to the volume of the 3 small spherical balls.

R D Sharma Solutions For Class 10 Maths Chapter 16 Surface Areas And Volumes ex 16.1 – 1

Now,

Cancelling out the common part from both sides of the equation we get,

(3)3 = (2)3 + (1.5)3 + r3

r3 = 33– 23– 1.53 cm3

r3 = 15.6 cm3

r = (15.6)1/3 cm

r = 2.5 cm

As diameter = 2 x radius = 2 x 2.5 cm

= 5.0 cm.

Thus , the diameter of the third ball is 5 cm

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