2026 · Q71
How many square metres of canvas (approximately) will be required to make a conical tent 3 m high so that a man 2 m tall may stand anywhere within a radius of 1 m from its centre without stooping?
Elementary MathematicsMensuration
- A36 m²
- B40 m²
- C44 m²
- D48 m²
Explanation
For a man 2 m tall to stand anywhere within 1 m of the centre, the cone's height at radial distance 1 m must be at least 2 m. With apex height 3 m, the height profile is h(r) = 3(1 − r/R), so 3(1 − 1/R) = 2 gives R = 3 m. The slant height is l = √(3² + 3²) = 3√2 ≈ 4.243 m, and the canvas needed is πRl = π·3·3√2 = 9π√2 ≈ 40 m², option B.