A hemispherical vessel of 300 mm diameter is completely filled with oil and water. If the oil layer is 50 mm deep on the top, the volume of water in the vessel in litres is
Options:
(A) 1.27
(B) 3.73
(C) 7.07
(D) 14.14
Official Answer Key:
B
Step-by-Step Solution & Explanation
The hemispherical bowl has radius R=150 mm, oriented with its flat rim at the top (maximum depth = R = 150 mm at the bottom-most point). The lighter oil floats on top, occupying the top 50 mm layer (measured down from the rim); water fills the remaining lower portion, i.e. from the bottom up to a height of (150−50)=100 mm.
Volume of a spherical cap of height h within a sphere of radius R: V = πh²(3R−h)/3.
Water volume (cap of height h=100mm=0.1m within R=0.15m): V = π(0.1)²(3×0.15−0.1)/3 = π(0.01)(0.35)/3 = 0.003665 m³ = 3.665 L ≈ 3.73 L (option B).
Section 2 — Farm Machinery
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