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An ice cream cone maker wants to build a more stable cone by increasing the diameter and decreasing the height of the cone. The cone currently has diameter dd centimeters and height hh, as shown. They want the height of the new cone to be h′h'. Which of the following is closest to the smallest radius the new cone can have so that the volume is at least the volume of the old cone?

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Q. An ice cream cone maker wants to build a more stable cone by increasing the diameter and decreasing the height of the cone. The cone currently has diameter dd centimeters and height hh, as shown. They want the height of the new cone to be h′h'. Which of the following is closest to the smallest radius the new cone can have so that the volume is at least the volume of the old cone?
  1. Calculate Volume of Cone: First, we need to calculate the volume of the original cone. The formula for the volume of a cone is V=(13)πr2hV = (\frac{1}{3})\pi r^2 h, where rr is the radius and hh is the height. Since the diameter is given, we would divide it by 22 to find the radius.

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