Question
A cone and a hemisphere have the same base radius and
the same height. If the total volume of both is 2,160 cm³, find the radius.Solution
Volume of cone = (1/3)πr²h Volume of hemisphere = (2/3)πr³ Total volume = (1/3)πr²h + (2/3)πr³ = 2160 Since base radius and height are the same, let h = r. (1/3)πr³ + (2/3)πr³ = 2160 (1/3 + 2/3)πr³ = 2160 πr³ = 2160 r³ = 2160 / π = 2160 / 3.14 ≈ 687.58 r ≈ 8.8 cm Correct Option: a) 8.8 cm
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