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

Options

• 100 π

• 75 π

• 60 π

• 50 π

Answer 1

In the given problem, Let the radius of smaller spherical balls which can be made from a bigger ball be xunits.

Here,

The radius of the bigger ball (r₁) = 10 cm

The radius of the smaller ball (r₂) = x cm

The number of smaller balls = 8

So, volume of the big ball is equal to the volume of 8 small balls.

Volume of the big balls = volume of the 8 small balls

`(4/3)pi r_1^3 = 8 (4/3) pi x^3`

`(4/3) pi (10)^3 =8 (4/3) pi x^3`

             `(10)^3 = 8 x^3`

             `x^3 = 1000/8`

Further, solving for x, we get,

`x=3sqrt(1000/8) `

`x = 10/2`

x = 5

Now, surface area of a small ball of radius 5 cm = `4 pi r^2` 

`= 4 pi(5)^2`

`= 100 pi`

Therefore, the surface area of the small spherical ball is `100 pi`.