Question

If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in sq.cm) is ?
A) 100 π
B) 101/Ï€
C) 99 π/12
D) 54/13Ï€

Answer 1

Hey.


Here is the answer.


A Solid ball of radius 10 cms are moulded into 8 solid balls of let radius r


So, Volume of Solid sphere = 4/3 π r^3

= 4/3 π 10^3


which will be equal to 8× 4/3 π r^3


or, 4/3 π 10^3 = 8 × 4/3 π r^3

or, 10^3 = 8 × r^3

or, 10^3 = 2^3 × r^3 = (2r)^3

so, 2r = 10

or, r = 10/2 = 5 cm


So, the radius of smaller balls will be 5 cm.


Now we know that surface area of a sphere

= 4 π r^2

So, surface area of each ball

= 4 π 5^2

= 100 π


So, (A) 100 π is the answer.


Thanks

Answer 2

hope it's helps you :)