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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 $d$ centimeters and height $h$ , as shown. They want the height of the new cone to be $h'$ . 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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Solve proportions: word problems

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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

d

centimeters and height

h

, as shown. They want the height of the new cone to be

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?

Calculate Volume of Cone: First, we need to calculate the volume of the original cone. The formula for the volume of a cone is $V = (\frac{1}{3})\pi r^2 h$ , where $r$ is the radius and $h$ is the height. Since the diameter is given, we would divide it by $2$ to find the radius.

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