Question
A cone has a height of 12 cm and a base radius of 5 cm.
A sphere with the same volume as the cone is constructed. What is the radius of the sphere?Solution
Volume of the cone = (1/3) * π * r² * h Where r = 5 cm and h = 12 cm: Volume of the cone = (1/3) * π * (5²) * 12 = (1/3) * π * 25 * 12 = 100π cm³. For the sphere, Volume = (4/3) * π * R³. Setting the volumes equal: (4/3) * π * R³ = 100π Cancel π: (4/3) * R³ = 100 R³ = 75 R = ∛ 75 ≈ 4.22 cm. Correct option: a) 4.2 cm
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