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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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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 Answer

  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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