Discussion
The curved surface area of a cone is 308 cm² and its slant height is 14 cm. Which of the following statements is true?
Answer: B
Start from the curved surface area to find the radius, taking \( \pi = \tfrac{22}{7} \).
\[ \pi r l = 308 \quad\Longrightarrow\quad \frac{22}{7} \times r \times 14 = 308 \]
\[ 44r = 308 \quad\Longrightarrow\quad r = 7 \text{ cm} \]
Now the total surface area adds the base:
\[ \text{TSA} = \pi r(l + r) = \frac{22}{7} \times 7 \times (14 + 7) = 22 \times 21 = 462 \text{ cm}^{2} \]
So the true statement is that the total surface area is 462 cm².
Checking the others: the radius is 7 cm, not 14 - 14 cm is the slant height. The height is \( \sqrt{l^{2} - r^{2}} = \sqrt{196 - 49} = \sqrt{147} \approx 12.1 \) cm, which is the square root of 147, not its square.
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