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
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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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