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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.
Solution
We have,
the radii r1 = 6 cm, r2 = 8 and r3 = 10 cm
Let the radius of the resulting sphere be R.
As,
Volume of resulting sphere = Volume of three metallic spheres
`rArr 4/3piR^3 = 4/3pir_1^3 +4/3pir_2^3 +4/3pir_3^3`
`rArr 4/3piR^3 = 4/3pi(r_1^3 + r_2^3 + r_3^3)`
`rArr R^3 = r_1^3 + r_2^3 + r_3^3`
`rArr R^3 = 6^3 +8^3 + 10^3`
`rArr R^3 =216 + 512+1000`
`rArr R^3 =1728`
`rArr R = root(3)(1728)`
`rArr R= 12 "cm"`
So, the radius of the resulting sphere is 12 cm.
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