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    Question

    A solid metal sphere of radius 6 cm is melted and recast

    into solid hemispheres of radius 3 cm. How many such hemispheres are formed?
    A 10 Correct Answer Incorrect Answer
    B 16 Correct Answer Incorrect Answer
    C 18 Correct Answer Incorrect Answer
    D 21 Correct Answer Incorrect Answer

    Solution

    Volume of sphere: V_sphere = (4/3)ฯ€Rยณ = (4/3)ฯ€ ร— 6ยณ = (4/3)ฯ€ ร— 216 = 288ฯ€ Volume of one hemisphere (radius 3 cm): V_hemi = (2/3)ฯ€rยณ = (2/3)ฯ€ ร— 3ยณ = (2/3)ฯ€ ร— 27 = 18ฯ€ Number of hemispheres = 288ฯ€ / 18ฯ€ = 16.

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