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 r2

Radius of sphere which is melted = r1 = 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 = πr3

8 × πr23 = πr13

8r23 = r13

Substituting values

8 × r23 = 103

8 × r23 = 1000

r23 =

r2 = = 5 cm

Surface area of sphere = 4πr2

surface area of small spheres made = 4πr22

= 4 × π × 52

= 4 × π × 25

= 100π cm2

Therefore, surface area of each sphere obtained is 100π cm2

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