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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
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Solution
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`.
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