Question
Download Solution PDFA cone is kept on a cylinder. The base of cone and cylinder are identical. The height of the conical part is 36 cm and height of the cylindrical part is 24 cm. If the diameter of the cone is 14 cm, then what is the volume of the solid?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Height of cone = 36 cm
Height of cylinder = 24 cm
Diameter = 14 cm ⇒ Radius = 7 cm
Formula used:
Volume of cone = (1/3) × π × r2 × h
Volume of cylinder = π × r2 × h
Total volume = Volume of cone + Volume of cylinder
Calculation:
Volume of cone = (1/3) × (22/7) × 72 × 36 = (1/3) × (22/7) × 49 × 36
⇒ = (22 × 49 × 36) / (3 × 7) = 38808 / 21 = 1848 cm³
Volume of cylinder = (22/7) × 72 × 24 = (22/7) × 49 × 24
⇒ = (22 × 49 × 24) / 7 = 25872 / 7 = 3696 cm³
Total volume = 1848 + 3696 = 5544 cm³
∴ Volume of the solid = 5544 cm³
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