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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