Two right circular cones have heights in a 1:2 ratio and base perimeters in a 3:4 ratio. What is the ratio of their volumes_________?
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Answer: C. 9:32
Explanation
Cone volume is proportional to the square of the base radius multiplied by height. Base perimeters ratio equals the base radii ratio, which is given as 3 to 4. Squaring radii and multiplying by height ratio yields a volume ratio of 9 to 32. Volume of a right circular cone equals one-third pi r squared times h. Base perimeter of a circular cone equals two pi r. Heights ratio for the two cones is given as 1 to 2 respectively.
Proportional reasoning in solid geometry helps scale volumetric capacities of containers. Industrial design uses volume ratios to compare storage vessel efficiencies. Calculations involving similar or related geometric solids are common in physics. Choosing 3:8 fails to apply the square of the radius ratio correctly. Choosing 9:16 omits the height ratio from the volumetric calculation. Choosing 9:64 applies an incorrect exponent to the radius or height variables.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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