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Mathematics

The number of balls of radius 1 cm that can be made from a sphere of radius 10 cm is

  1. 100

  2. 1000

  3. 10000

  4. 100000

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Answer

Radius of sphere (R) = 10 cm.

Radius of ball (r) = 1 cm

Let number of balls formed be n.

Since a big sphere is divided into small balls.

Volume of sphere = n × Volume of each ball.

43πR3=n×43πr3\dfrac{4}{3}πR^3 = n \times \dfrac{4}{3}πr^3

Multiplying both sides by 34π\dfrac{3}{4π}.

⇒R3=nr3⇒n=R3r3⇒n=10313⇒n=1000.\Rightarrow R^3 = nr^3 \\[1em] \Rightarrow n = \dfrac{R^3}{r^3} \\[1em] \Rightarrow n = \dfrac{10^3}{1^3} \\[1em] \Rightarrow n = 1000.

Hence, Option 2 is the correct option.

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