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    Question

    A sphere has a diameter of 10 cm. A cone with a height

    of 10 cm and a radius of 5 cm is removed from the sphere. What is the volume of the remaining solid?
    A 300π cm³ Correct Answer Incorrect Answer
    B 250/3π cm³ Correct Answer Incorrect Answer
    C 230/3π cm³ Correct Answer Incorrect Answer
    D 150π cm³ Correct Answer Incorrect Answer

    Solution

    Volume of the sphere = (4/3) * π * (r³) Where r = 5 cm (radius): = (4/3) * π * (5³) = (4/3) * π * 125 = (500/3)π cm³. Volume of the cone = (1/3) * π * r² * h = (1/3) * π * (5²) * 10 = (1/3) * π * 25 * 10 = (250/3)π cm³. Remaining volume = Volume of sphere - Volume of cone = (500/3)π - (250/3)π = (250/3)π cm³. Correct option: b) 250/3π cm³

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