Question

    A solid cylinder has a radius of 3 cm and a height of 10

    cm. If it is melted and recast into a cone with a base radius of 3 cm, what will be the height of the cone?
    A 25 cm Correct Answer Incorrect Answer
    B 30 cm Correct Answer Incorrect Answer
    C 15 cm Correct Answer Incorrect Answer
    D 20 cm Correct Answer Incorrect Answer

    Solution

    Volume of the cylinder = π * r² * h = π * (3²) * 10 = π * 9 * 10 = 90π cm³. Volume of the cone = (1/3) * π * r² * h Let the height of the cone be h: 90π = (1/3) * π * (3²) * h Cancel π: 90 = (1/3) * 9 * h 90 = 3h h = 30 cm. Correct option: b) 30 cm

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