The curved surface area of a cone of height 12 m is 204(2)/(7) m2. Its slant height is ______.

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The curved surface area of a cone of height 12 m is 204(2)/(7) m2. Its slant height is 13 m. Explanation: The curved surface area of a cone is given by $\pi$rl = $\frac{1430}{7}$, which simplifies to r $\times$ l = 65. Using the relation l2 = r2 + h2 with heigh h = 12m, substituting r = 5 m and l = 13 m satisfies both equations (5 $\times$ 13 = 65 and 132 = 52 + 122) Therefore, the slant height is 13m.

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