What length of tarpaulin 3 m wide is required to make a conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that is required for stitching margins and wastage in cutting is 20 cm.
Step-by-step solution
To find: Length of tarpaulin
Idea: The tent uses only the curved surface. Area of tarpaulin = length × width, so length = area ÷ 3, then add the 20 cm extra.
- l = √(82 + 62) = √100 = 10 m.1 mark
- Area of tarpaulin = CSA = πrl = 3.14 × 6 × 10 = 188.4 m2.1 mark
- Length needed = area ÷ width = 188.4 ÷ 3 = 62.8 m.1 mark
- Add the extra 20 cm = 0.2 m: 62.8 + 0.2 = 63 m. (With π = 227: 62.86 + 0.2 ≈ 63.06 m.)1 mark
Check: 63 m × 3 m = 189 m2 = 188.4 m2 for the tent + 0.6 m2 extra ✓.
Answer to write in the exam
l = √(82 + 62) = 10 m
Area = πrl = 3.14 × 6 × 10 = 188.4 m2
Length = 188.4 ÷ 3 = 62.8 m
∴ Length required = 62.8 + 0.2 = 63 m
Common mistakes that cost marks
- Adding 20 (cm) as 20 m, or forgetting to convert it to 0.2 m.
- Dividing the area by the height 8 m instead of the width 3 m.
- Using TSA (adding the floor).
How this can come in the exam
A scout troop makes a conical tent of base radius 2.1 m and height 2.8 m from canvas 1.4 m wide.
(i) Find the slant height. (ii) Find the canvas area. (iii) Find the length of canvas needed. (iv) If canvas costs ₹ 70 per metre, find the cost. (π = 227)
Show answer
(i) √(2.12 + 2.82) = √(4.41 + 7.84) = √12.25 = 3.5 m (1 mark). (ii) 227 × 2.1 × 3.5 = 23.1 m2 (1 mark). (iii) 23.1 ÷ 1.4 = 16.5 m (1 mark). (iv) 16.5 × 70 = ₹ 1155 (1 mark).Try one yourself
How many metres of cloth 1.1 m wide will be needed for a conical tent of radius 7 m and slant height 12 m (no extra)? (π = 227)
Show answer
Area = 227 × 7 × 12 = 264 m2; length = 264 ÷ 1.1 = 240 m.
More questions like this
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