Question
A right circular cone has a base radius of 4 cm and a
height of 9 cm. If a cylindrical hole of radius 2 cm is drilled through the axis of the cone, what is the volume of the remaining solid?Solution
Volume of the cone = (1/3) * π * r² * h = (1/3) * π * (4²) * 9 = (1/3) * π * 16 * 9 = 48π cm³. Volume of the cylindrical hole = π * r² * h Where r = 2 cm and height of the cone = 9 cm: Volume of the hole = π * (2²) * 9 = π * 4 * 9 = 36π cm³. Remaining volume = Volume of cone - Volume of hole = 48π - 36π = 12π cm³. Correct option: a) 12π cm³
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