A cylindrical container of radius 6 cm and height 15 cm is full of ice cream. The ice cream is served into 10 identical cones, each topped by a hemisphere of the same radius as the cone, and every cone is filled exactly. If the height of each cone is 4 times its radius, find that radius in cm.

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Accepted Answer

3. Container volume = π × 36 × 15 = 540π cm³. For one serving of radius r the cone holds (1/3)πr²(4r) = (4/3)πr³ and the hemisphere holds (2/3)πr³, together 2πr³. Ten servings give 20πr³ = 540π, so r³ = 27 and r = 3 cm.

A cylindrical container of radius 6 cm and height 15 cm is full of ice cream. The ice cream is served into 10 identical cones, each topped by a hemisphere of the same radius as the cone, and every cone is filled exactly. If the height of each cone is 4 times its radius, find that radius in cm.

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