A conical tent has base radius 6 m and height 8 m. Find the area of canvas needed and the volume of air inside it. (Take π = 3.14.)
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Write what is given and what is to be found r = 6 m, h = 8 m. To find: canvas (the CSA) and the volume of air.
2 · Draw the figure Draw a cone. Mark the height h = 8 m from the tip to the centre of the base, the radius r = 6 m, and the slant height l along the side. Show the right angle at the centre.
3 · Write the formulas l = √(h² + r²); CSA = πrl; volume = (1/3)πr²h.
4 · Find the slant height
l = √(8² + 6²) = √(64 + 36)
= √100 = 10 m
5 · Find the canvas
CSA = 3.14 × 6 × 10
= 188.4 m²
6 · Find the volume of air
V = 1/3 × 3.14 × 6 × 6 × 8
= 3.14 × 96 = 301.44 m³
7 · Check and box the answer Canvas = 188.4 m²; volume of air = 301.44 m³. The floor has no canvas, so the CSA is used, not the TSA.
Scoring tip: A tent, a cap or a funnel has no base, so the area asked is the CSA. Find l first and write it on your figure.
