NumericalHard4 marks
6
A hemispherical and a conical hole is scooped out of a solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows: The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm. Give your answer correct to the nearest whole number. Take π=22 7 .
Topic: Mensuration of solids
Previous-year question practice database
Answer
Exam answer
Cylinder: r=3 cm, h=7 cm. Cone: r=3 cm, h=3 cm. Hemisphere: r=3 cm. π=22/7.
Remaining volume = cylinder − cone − hemisphere = πr²(7) − (1/3)πr²(3) − (2/3)πr³ = 198 − 198/7 − 396/7 = 792/7 ≈ 113.14 cm³.
Nearest whole number:
Answer: 113 cm³.
Explanation
Subtract the volumes of the conical and hemispherical holes from the cylinder.
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