Multiple choice

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

  1. 100 $\displaystyle \pi$
  2. 75 $\displaystyle \pi $
  3. 60 $\displaystyle \pi $
  4. 50 $\displaystyle \pi $
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A Correct answer
Explanation

The volume of the original sphere is (4/3) * pi * 10^3. When divided into 8 equal spheres, each small sphere has a volume of (1/8) * (4/3) * pi * 10^3 = (4/3) * pi * 5^3, meaning the radius of each small sphere is 5 cm. The surface area of each small sphere is 4 * pi * 5^2 = 100 * pi.

AI explanation

The total volume of the 8 balls equals the volume of the original sphere. The volume of the original sphere is 4/3 times pi times 10 cubed, which is 4000pi/3. Setting 8 times 4/3 times pi times r cubed equal to 4000pi/3 gives a new radius of 5 cm. The surface area of each new ball is 4 times pi times 5 squared, which is 100 pi.

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