A cone has a slant height of 12 cm and a base radius of 4 cm. Find its curved surface area.
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Answer: C. 48 π cm2
Explanation
The curved surface area of any right circular cone is calculated by multiplying pi, radius, and slant height. Substituting the given base radius of four centimeters and slant height of twelve centimeters into the formula. Multiplying pi by four and twelve yields forty-eight pi square centimeters for the curved surface area. Curved surface area excludes the circular base area and considers only the lateral conical wrapping surface. Geometric formulas for cones relate radius, height, slant height, and pi through standard algebraic expressions. Square units are used for all two-dimensional surface area measurements in metric geometric calculations.
Manufacturing engineers calculate sheet metal requirements when producing conical funnels or traffic safety cones. Architects determine material surface coatings needed for conical roof structures on historical buildings. Packaging designers compute label areas required for wrapping conical food containers and beverage cups. Option A suggests seventy-four pi square centimeters which represents an arithmetic calculation error. Option B suggests thirty-six pi square centimeters which underestimates the product of radius and slant height. Option D suggests twenty-four pi square centimeters which halves the correct calculated surface area value.
- Subject
- Mathematics
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- Mathematics
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- Difficulty
- medium
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