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?
    A 64 Correct Answer Incorrect Answer
    B 72 Correct Answer Incorrect Answer
    C 80 Correct Answer Incorrect Answer
    D 96 Correct Answer Incorrect Answer

    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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