Q. 84.8( 4 Votes )

# Eight spheres of equal radii are obtained by melting a metallic sphere of radius 10 cm. Find the surface area of each sphere thus obtained.

Answer :

Let the radius of small spheres formed be r_{2}

Radius of sphere which is melted = r_{1} = 10 cm

As the sphere is melted and then the small spheres are made from the same amount of melted sphere, therefore, the volume remains same

8 small spheres are made

Volume of sphere = πr^{3}

⇒ 8 × πr_{2}^{3} = πr_{1}^{3}

⇒ 8r_{2}^{3} = r_{1}^{3}

Substituting values

⇒ 8 × r_{2}^{3} = 10^{3}

⇒ 8 × r_{2}^{3} = 1000

⇒ r_{2}^{3} =

⇒ r_{2} = = 5 cm

Surface area of sphere = 4πr^{2}

⇒ surface area of small spheres made = 4πr_{2}^{2}

= 4 × π × 5^{2}

= 4 × π × 25

= 100π cm^{2}

Therefore, surface area of each sphere obtained is 100π cm^{2}

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