2023 · Q81
A sphere of radius 5 cm is dropped in a right circular cylindrical vessel partly filled with water. The radius of the cylindrical vessel is 10 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?
Elementary MathematicsMensuration
- A5/3 cm
- B5/2 cm
- C1 cm
- D5/6 cm
Explanation
The water level rises by the volume the sphere displaces divided by the vessel's cross-sectional area. The sphere's volume is (4/3)π·5³ = 500π/3 cm³. The cylindrical vessel of radius 10 cm has cross-section π·10² = 100π cm². The rise is therefore (500π/3)/(100π) = 5/3 cm, option (A).