Discussion
A cone has a circular base of radius 5 cm and a height of 12 cm. Its curved surface area is
Answer: A
The curved surface needs the slant height, so find it by Pythagoras first.
\[ l = \sqrt{r^{2} + h^{2}} = \sqrt{5^{2} + 12^{2}} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ cm} \]
\[ \text{CSA} = \pi r l = 3.1416 \times 5 \times 13 \]
\[ = 204.2 \approx 204 \text{ cm}^{2} \]
5–12–13 is a Pythagorean triple, which is why the slant height comes out whole. Including the base would add \( \pi r^{2} = 78.5 \) cm² and give the total surface area of about 283 cm².
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