NumericalModerate2 marks
3(ii)
An eye drop bottle is prepared consisting of a hemisphere, a cylinder and a conical cap, as shown in the given diagram. Height of the cylindrical and conical parts are each, equal to the diameter (7 cm). Find the :
volume of the liquid medicine (shaded part) in the bottle. Give your answer to the nearest whole number. (Use π = 22/7 )
Topic: Mensuration
Previous-year question practice database
Answer
Exam answer
Diameter = 7 cm ⇒ r = 3.5 cm. Cylinder height h = 7 cm. π = 22/7.
Volume of cylinder = πr²h = 22/7 × (3.5)² × 7 = 269.5 cm³.
Volume of hemisphere = (2/3)πr³ = (2/3) × 22/7 × (3.5)³ ≈ 89.83 cm³.
Liquid volume = 269.5 − 89.83 = 179.67 cm³ ≈ 180 cm³.
Answer: 180 cm³.
Explanation
The liquid occupies the cylindrical volume except for the hemispherical part shown inside the bottle.
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