A sphere of diameter 14 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 14 cm. If the sphere is completely submerged in water, then how much will the level of water rise?
A.7/3 cm✓ Correct
B.8/3 cm
C.14/3 cm
D.16/3 cm
Explanation
Volume of sphere = (4/3)π·r³ = (4/3)π·7³ = (4/3)π·343 = 1372π/3 cm³. This equals the rise in water level h times the area of cylinder base: π·R²·h = π·14²·h = 196π·h. So 196π·h = 1372π/3, giving h = 1372/(3·196) = 7/3 cm.
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