Question
A solid metallic cone with a radius of 6 cm and height
of 12 cm is melted and recast into smaller cones with a radius of 3 cm and a height of 4 cm. How many smaller cones can be formed?Solution
Volume of the larger cone = (1/3)πr²h = (1/3) × (22/7) × 6² × 12. = (1/3) × (22/7) × 36 × 12 cm³. Volume of a smaller cone = (1/3)πr²h = (1/3) × (22/7) × 3² × 4. = (1/3) × (22/7) × 9 × 4 cm³. Number of smaller cones = (1/3) × (22/7) × 36 × 12/ (1/3) × (22/7) × 9 × 4 = 12 Correct answer: c) 12.
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