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A cone has base radius 15 cm and vertical height 20 cm. A plane parallel to the base cuts off the top, and the circle of the cut has radius 6 cm. Find the height of the frustum left behind, in cm.

Competition practiceAreas & Volumes
  • A8
  • B9
  • C14
  • D12

Step-by-Step Solution

The small cone removed is similar to the whole cone, so its height ÷ 20 = 6/15 = 0.4, giving a height of 8 cm. The frustum keeps the rest: 20 − 8 = 12 cm.
Answer: D) 12

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