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Question

Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere(in cm).


A

12

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B

21

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C

18

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D

15

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Solution

The correct option is A

12


Radius of first sphere =r1=6 cm
Radius of second sphere =r2=8 cm
Radius of third sphere =r3=10 cm
Let radius of resulting sphere be r cm.
According to given condition, we have
Volume of first sphere + Volume of second sphere + Volume of third sphere = Volume of resulting sphere
43π(r1)3+43π(r2)3+43π(r3)3=43πr3

43[(r1)3+(r2)3+(r3)3]=43r3

(63+83+(10)3)=r3

(216+512+1000)=r3

r3=1728

r=12 cm


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