The circumference of the base of a 10 m high conical tent is 44 meters. What…

Concept

The canvas of a conical tent forms only its slanted (lateral) wall, so the canvas area equals the curved surface area of a cone, CSA = πrl, where r is the base radius and l is the slant height. The slant height links the radius and the vertical height by l = √(r2 + h2). The base circumference gives the radius through C = 2πr.

Application

1. Find the radius from the circumference: 2πr = 44, so r = 44 ÷ (2 × 22/7) = 44 × 7 ÷ 44 = 7 m.

2. Find the slant height: l = √(r2 + h2) = √(72 + 102) = √(49 + 100) = √149 ≈ 12.21 m.

3. Apply the formula: CSA = πrl = (22/7) × 7 × 12.21 = 22 × 12.21 ≈ 268.5 m2.

Cross-check

Verify the slant height independently: l2 = 49 + 100 = 149, and 12.212 ≈ 149.1, confirming l ≈ 12.21 m. Multiplying by πr = 22 then gives 22 × 12.21 ≈ 268.5 m2, so the canvas needed is about 268.5 m2.