A cylindrical vessel has a 7 cm radius and 3 cm height. Find its total surface area.
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Answer: C. 440 sq cm
Explanation
The total surface area formula for a closed cylinder requires calculating both circular bases and curved walls. Substituting radius seven and height three into two pi r times h plus r yields the correct value. Multiplying two by twenty two sevenths by seven by ten produces four forty square centimeters. A cylinder consists of two parallel circular bases connected by a curved lateral surface area. The lateral surface area formula is two times pi times radius times height measurement. The combined area of both circular ends equals two times pi times radius squared.
Manufacturing engineers calculate total surface area to determine sheet metal requirements for cylindrical containers. Painter calculations require surface area measurements to estimate coating volumes for cylindrical silos. Packaging designers evaluate material costs for cylindrical beverage cans based on total surface area. Option a represents only the lateral surface area plus one base instead of both bases. Option b corresponds to an incomplete formula calculation missing the height component addition. Option d calculates a value that is much too small for the given radius and height.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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