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QuestionMathematics
What is the formula for the lateral surface area of 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 Cylinder's Lateral Surface
The lateral surface of a cylinder is the curved surface area around the cylinder, excluding the top and bottom circular bases.
Step 3:: Identify the Components
To calculate the lateral surface area, we need: - Circumference of the circular base - Height of the cylinder
Step 4:: Derive the Lateral Surface Area Formula
The lateral surface area is calculated by multiplying the circumference of the base by the height of the cylinder.
Step 5:: Write the Formal Formula
- $$h$$ is the height of the cylinder
The lateral surface area formula is: Where:
Final Answer
The formula for the lateral surface area of a cylinder is A_{lateral} = 2\pi r h.
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