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A water tank is hemisphere-on-cylinder shape with hemisphere radius 1.5 m and total height 2.5 m. The volume of the cylindrical portion equals:
Answer & Solution
Correct answer: A.
1. The cylindrical portion sits below the hemisphere with height = 2.5 − 1.5 = 1.0 m.
2. Wait — the hemisphere sits at the bottom of the tank. Height of cylinder = total − hemisphere radius = 2.5 − 1.5 = 1.0 m.
3. Volume of cylinder = π × (1.5)² × 1.0 = 2.25 π m³.
4. So the cylindrical part holds 2.25 π m³.
5. The full tank also includes a hemispherical (2/3) π (1.5)³ = 2.25 π m³ portion, giving 4.5 π m³ total.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._
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