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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 the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.

A
1cm
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B
3cm
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C
4cm
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D
5cm
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Solution

The correct option is D 5cm
Volume of the large ball of radius 3 cm
=43×227×3×3×3=7927cm3
Total volume of the two smaller balls of radii 1.5 cm and 2 cm
43×227×32×32×32+43×227×2×2×2
[V=43πr3]
43×227(278+8)=1433cm3
Volume of the third ball
=79271433=2376100121
137521cm3
Let r be the radius of the 3rd ball
43×227×r3=137521
r3137521×34×722=1258
r=31258=52cm
Hence diameter =2r=2×52=5cm

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