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

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If you open math book you will find a lot of mathematical questions but
you should have solve this question.
It is from class 10 rd sharma chapter 16 mensuration .

In this question we have to find the diameter of the third ball
given that a spherical ball of radius 3 cm is melted and
recast into three spherical balls.The radii of two of the
balls are 1.5 cm and 2 cm.

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1. Given,

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 – 3

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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