Question
The radius of the base of a cone is 12 cm, and its
height is 16 cm. The cone is melted and recast into smaller cones of radius 3 cm and height 4 cm. How many such smaller cones can be made?Solution
Volume of a cone = (1/3)πr²h. Volume of the large cone = (1/3) × π × 12² × 16 = (1/3) × π × 144 × 16 = 768π cm³. Volume of a smaller cone = (1/3) × π × 3² × 4 = (1/3) × π × 9 × 4 = 12π cm³. Number of smaller cones = Volume of the large cone / Volume of a smaller cone = 768π / 12π = 64.
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