Multiple choice

A cylindrical vessel of radius 16 cm contains water to a depth of 20 cm. A solid spherical metallic ball is dropped into the vessel which is fully submersed and raises the level of the water in the vessel by 9 cm. What is the surface area (in cm²) of the ball? (Assume no overflow of water)

  1. 288π

  2. 784π

  3. 324π

  4. 576π
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The volume of water displaced equals the volume of the spherical ball. Volume of cylinder = πr²h = π × 16² × 9 = 2304π cm³. For a sphere, V = (4/3)πr³, so r³ = (2304 × 3)/4 = 1728, giving r = 12 cm. Surface area = 4πr² = 4π × 144 = 576π cm².

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