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प्रश्न
If r1 and r2 be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new sphere is \[\left( r_1^3 + r_2^3 \right)^\frac{1}{3}\].
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उत्तर
Volume of first sphere `=4/3 pir_1^3`
Volume of second sphere `=4/3 pir_2^3`
Total volume of new sphere `=(4/3 pir_1^3 +=4/3 pir_2^3)`
Say of radius of new sphere = r3
Volume of new sphere `=4/3 pir_3^3`
Hence,
`4/3 pir_3^3 =4/3 pir_1^3+4/3 pir_2^3`
`4/3 pir_3^3 =4/3 pi(r_1^3+r_2^3)`
`r_3^3 = r_1^3 +r_2^3`
So, radius of new sphere `r_3 = (r_1^3 + r_2^3)^(1/3)`.
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