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2. 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.

2. 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.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8740 Points
3 months ago
For Sphere 1: Radius (r1) = 6 cm ∴ Volume (V1) = (4/3)×π×r13 For Sphere 2: Radius (r2) = 8 cm ∴ Volume (V2) = (4/3)×π×r23 For Sphere 3: Radius (r3) = 10 cm ∴ Volume (V3) = (4/3)× π× r33 Also, let the radius of the resulting sphere be “r” Now, Volume of resulting sphere = V1+V2+V3 (4/3)×π×r3 = (4/3)×π×r13+(4/3)×π×r23 +(4/3)×π×r33 r3 = 63+83+103 r3 = 1728 r = 12 cm

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