A cylinder has a 2r radius and a 3r height. Find its curved surface area.
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Answer: C. 12 πr2 sq units
Explanation
The curved surface area formula requires multiplying two by pi, the radius, and the height. Substituting the given dimensions into the formula yields two multiplied by pi by two r by three r. Multiplying these numerical coefficients together results in the correct final product of twelve pi r squared. A cylinder consists of two parallel circular bases and one continuous curved lateral surface connecting them. The lateral surface area excludes the top and bottom circular bases from the total geometric calculation. Basic algebraic multiplication rules apply when combining coefficients and variables in polynomial geometric expressions.
Eighteen pi r squared arises from incorrectly multiplying the numerical coefficients without proper algebraic simplification steps. Three pi r squared underestimates the curved area by failing to distribute all dimensional factors correctly through multiplication. An answer of six pi r squared completely misses the multiplication step involving the individual radius components.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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