A cylindrical pillar has a curved surface area of 264 m2 and a volume of 924 m3. Find the ratio of its diameter to height.
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Answer: B. 7 : 3
Explanation
Dividing the volume of the cylindrical pillar by its curved surface area yields half the radius value. Multiplying this half-radius result by two gives a radius of seven, making the diameter fourteen meters. Calculating the height using the curved surface area formula gives three meters, resulting in a ratio of seven to three. Curved surface area of a cylinder equals two pi r h, while volume equals pi r squared h. Dividing volume by curved surface area provides a direct shortcut to finding the cylinder radius. Ratio of diameter to height compares the full width of the cylinder base to its vertical height.
Architects and civil engineers calculate cylindrical column dimensions for load-bearing building designs. Manufacturing plants use surface area and volume formulas to estimate material requirements for pillars. Geometric ratio problems test a student's ability to manipulate algebraic formulas efficiently. Option A reverses the diameter-to-height ratio, incorrectly placing the smaller dimension first. Option C results from using incorrect radius and height values in the final ratio comparison. Option D alters the correct proportional relationship by swapping the calculated terms.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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