A cone of radius 9 cm and height 12 cm is cut into two parts by a plane parallel to its base, at a height of 4 cm from the vertex. Find the volume of the frustum formed.
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 312πcm3
Volume of whole cone = (1/3) × π × r2 × h = (1/3) × π × 92 × 12
= (1/3) × π × 81 × 12 = 324π cm3
The small cone cut from the top has height = 4 cm
By similarity,
Radius of small cone = 9 × 4/12 = 3 cm
Volume of small cone = (1/3) × π × 32 × 4 = (1/3) × π × 9 × 4 = 12π cm3
Volume of frustum = 324π − 12π = 312π cm3
Therefore, the volume of the frustum is 312π cm3.