Question

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq. cm) is
A. 100π
B. 75π
C. 60π
D. 50π

Answer 1

Given : A solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius.

We know that, Volume of sphere ,V =   (4/3)πr³

Radius , R = 10 cm

Let the radius of spherical solid ball be r .

V of  1 spherical solid ball = (4/3)πR³ = (4/3)π × 10³

V of 8 spherical solid balls = 8 × (4/3)π × r³

Volume of  1 spherical solid ball = volume of  8 spherical solid balls

(4/3)π × 10³ = 8 × (4/3)π × r³

10³ = 8r³

r³ = 1000/8

r = ³√1000/8

r = 10/2

Radius of spherical solid ball , r = 5 cm

We know that, Surface area of a sphere = 4πr²

Then, the surface area of each sphere,S = 4 × π ×5²

S  = 4 × π × 25

S = 100π

Hence the surface area of each ball (in sq. cm) is 100π.

Option (A) 100π is correct.

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