Multiple choice

A conical tent has a height of 12 metres and a floor area of 616 square metres. If the canvas used for the tent is 1.2 metres wide, what is the approximate length of canvas required to build the tent?

  1. 576.13 m

  2. 676.13 m

  3. 746.36 m

  4. 846.43 m

  5. a
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area = pi * r^2 = 616. r^2 = 616 * 7 / 22 = 196, so r = 14. Slant height l = sqrt(r^2 + h^2) = sqrt(14^2 + 12^2) = sqrt(196 + 144) = sqrt(340) approx 18.44. Lateral surface area = pi * r * l = (22/7) * 14 * 18.44 = 44 * 18.44 = 811.36. Length of canvas = Area / width = 811.36 / 1.2 = 676.13.

AI explanation

Given the floor area of the circular base is 616 square metres, the radius is found by πr^2 = 616, which gives r = 14 m. Using the Pythagorean theorem, the slant height of the conical tent is calculated as the square root of (12^2 + 14^2), equating to 18.44 m. The area of the canvas equals the curved surface area of the cone (πrl), which is (22/7) * 14 * 18.44, or 811.36 square metres. Dividing this area by the canvas width of 1.2 m gives an approximate length of 676.13 m.

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