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.​

Answer 1

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Answer 2

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For Sphere 1:

Radius (r1) = 6 cm

∴ Volume (V1) = (4/3) × π× r1^3

For Sphere 2:

Radius (r2) = 8 cm

∴ Volume (V2) = (4/3) × π × r2^3

For Sphere 3:

Radius (r3) = 10 cm

∴ Volume (V3) = (4/3) × π× r3^3

Also,

let the radius of the resulting sphere be “r”

Now,

Volume of resulting sphere

= V1+ V2 + V3

(4/3)× π× r^3 = (4/3)× π× r1^3 + (4/3)× π× r2^3 + (4/3) × π× r3^3

r^3 = 6^3 + 8^3 + 10^3

r^3 = 1728

r = 12 cm