Multiple choice

A sphere of 80 cm diameter is dropped into a cylindrical vessel of 40 cm radius, partially filled with water. The level of water rises by 'a'. What is the value of 'a'?

  1. 53.33 cm

  2. 50.33 cm

  3. 40 cm

  4. 20 cm

  5. 80 cm
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A Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 40^3 = 85333.33 * pi. Volume of water rise in cylinder = pi * R^2 * a = pi * 40^2 * a = 1600 * pi * a. Equating them: 1600 * a = 85333.33, so a = 53.33 cm.

AI explanation

The volume of the displaced water equals the volume of the dropped sphere, giving the formula (40)^2 h = (4/3) *(40)^3. Solving for h yields h = 160/3, which is 53.33 cm. The value of a is 53.33 cm.

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