Question

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

Options

• 11 m

• 13 m

• 14 m

• 16 m

Answer 1

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 πrl = `1430/7`, which simplifies to r × l = 65. Using the relation l2 = r2 + h2 with heigh h = 12m, substituting r = 5 m and l = 13 m satisfies both equations (5 × 13 = 65 and 13² = 5² + 12²)

Therefore, the slant height is 13m.