NumericalModerate3 marks
From a solid wooden cylinder of height 28 cm and diameter 6 cm, two conical cavities are hollowed out. The diameters of the cones are also of 6 cm and height 10.5 cm. Taking π = 22/7 find the volume of the remaining solid.
Topic: Mensuration
Previous-year question practice database
Answer
Exam answer
volume of remaining solid = 594 cm
Explanation
Dimension of cylinder Height (h) = 28 cm Diameter(2r) = 6 cm Dimension of conical cavities Height (H) = 10.5 cm diameter (2r) = 6 cm Volume of remaining solid = Volume of cylinder – 2 × Volume of cavity = π π r h r H 2 2 − × = πr h 2 2 −
H = 3 3 28 10 5 × × − × ( . ) = 3 3 28 7 × × ( ) − = 3 3 21 × × × = 22 × 3 ×3× 3 =594 cm Hence, volume of remaining solid = 594 cm
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