Question

The curved surface area of a cylinder depends on:

• A. \( 2\pi r^2 \)
• B. \( \pi r^2 h \)
• C. \( 2\pi rh \)
• D. \( 4\pi r^2 \)

Hint:

Imagine "unrolling" the curved side of a cylinder. It forms a rectangle with width equal to the height (\( h \)) and length equal to the circumference of the circle (\( 2\pi r \)). Area = \( L \times W = 2\pi r \times h \).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Identify the formula for the Curved Surface Area (CSA) of a right circular cylinder.

Step 2: Detailed Explanation:
A cylinder has a circular base with radius \( r \) and a height \( h \).
- The area of the circular base is \( \pi r^2 \).
- The volume of the cylinder is \( \pi r^2 h \).
- The circumference of the base is \( 2\pi r \).
- The curved surface area is the area of the side surface, which is the base circumference multiplied by the height.
\[ CSA = 2\pi r \times h = 2\pi rh \] - The total surface area (TSA) would be \( 2\pi rh + 2\pi r^2 = 2\pi r(r + h) \).

Step 3: Final Answer:
The formula for the curved surface area is \( 2\pi rh \).