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Question

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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Solution

Given that radius of the spherical ball r = 3 cm.

We know that the volume of the sphere =43πr3=43×227×(3)3=43×227×27=4×22×97=7927=113.1428 cm3


Given radii of the 1st sphere = 1.5 cm

Volume of the 1st sphere =43πr3=43×227×(1.5)3=43×227×3.375=14.1428.


Given radii of the 2nd sphere = 2 cm.

the volume of the 2nd sphere =43πr3=43×227×(2)3=33.5238.


Volume of the two small spheres = 14.1428 + 33.5238

= 47.6666.


Volume of the third sphere = 113.1428 - 47.6666

= 65.4762 cm3.


Let the radius of the third be r cm.

43πr3=65.476243×227×r3=65.4762r3=65.4762×722×34=65.4762×2188=1375.000288=15.62500r3=15.62500r=315.62500=2.5 cm


Therefore the radius of the third ball = 2.5 cm


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