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?
Answer
The correct answer is A: 7/3 cm. 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.
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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