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QuestionMathematics
Provide the formula to calculate the surface area of half a cylinder.
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Surface Area Components
The surface area of a half cylinder consists of three parts: - Curved surface area - Circular base - Flat (cut) surface
Step 3:: Recall the Cylinder Dimensions
- $$h$$ = height of the cylinder
Let:
Step 4:: Calculate Curved Surface Area
A_{curved} = \frac{1}{2} \times 2\pi rh = \pi rh
The curved surface area of a half cylinder is half the full curved surface area of a complete cylinder.
Step 5:: Calculate Base Area
A_{base} = \frac{1}{2} \pi r^{2}
The base area is half a circle:
Step 6:: Calculate Flat Surface Area
A_{flat} = hr
Step 7:: Total Surface Area Calculation
A_{total} = \pi rh + \frac{1}{2} \pi r^{2} + hr
Total surface area of half a cylinder:
Final Answer
The formula for the surface area of a half cylinder is A = \pi rh + \frac{1}{2} \pi r^{2} + hr, where r is the radius and h is the height.
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