CDS 2025 · PYQ · Mensuration / Frustum Volume · medium
A frustum of a right cone has a top of diameter 2k, bottom of diameter 2·5k and height k. What is the volume of the frustum?
- A.61πk³/48✓ Correct
- B.59πk³/48
- C.57πk³/48
- D.53πk³/48
Volume of frustum = (πh/3)(R² + r² + Rr). With r = k, R = 5k/4, h = k: V = (πk/3)(25k²/16 + k² + 5k²/4) = (πk/3)(25k²/16 + 16k²/16 + 20k²/16) = (πk/3)(61k²/16) = 61πk³/48.
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