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Metallic spheres of radii 6cm 8cm and 10cm respectively are melted to form a single solid Sphere Find the radius of the resulting sphere

Posted by Santu Choudhary 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Sum of the volumes of three given spheres = {tex}\frac43\mathrm\pi{/tex}[(6)³ + (8)³ + (10)³]
= {tex}\frac43\mathrm\pi{/tex}[216 + 512 + 1000]
= {tex}\frac43\mathrm\pi{/tex} × 1728 = 4{tex}\pi{/tex} × 576 = 2304π cm³
Let R be the radius of single solid sphere, since volume remains the same
∴ {tex}\frac43\mathrm\pi{/tex}R³ = 2304 {tex}\pi{/tex}
⇒ R³={tex}\frac{2304\times3}4=\;576\times3{/tex}
⇒ R³= 1728 = (12)³
∴ R = 12 cm

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