Discussion
A right-circular cone having slant height 37 cm and diameter of base 24 cm is melted and reshaped into a right-circular cone of radius 6 cm. What is the height of the new cone?
Answer: B
The first cone has radius 12 cm and slant height 37 cm, so its height is the square root of 37 squared minus 12 squared, which is 35 cm.
\[ \tfrac{1}{3}\pi (12)^2 (35) = \tfrac{1}{3}\pi (6)^2 h \]
\[ 144 \times 35 = 36h \Rightarrow h = 140 \]
The new cone is 140 cm high. The height of 148 cm would come from taking the volume in terms of the slant height, and 150 and 160 cm do not fit.
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