Discussion

The curved surface area of a cone is

Answer: C

Unrolled flat, a cone's curved surface is a sector of a circle of radius \( l \) whose arc is the base circumference \( 2\pi r \). Its area is

\[ \text{CSA} = \frac{1}{2} \times \text{arc} \times \text{radius} = \frac{1}{2} \times 2\pi r \times l = \pi r l \]

The total surface area adds the circular base:

\[ \text{TSA} = \pi r l + \pi r^{2} = \pi r (l + r) \]

Note that the slant height \( l \) is used here, not the perpendicular height \( h \); the two are related by \( l^{2} = r^{2} + h^{2} \).

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