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Question
What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. [Use π = 3.14]
Solution
Height (h) of conical tent = 8 m
Radius (r) of base of tent = 6 m
Slant height (l) of tent = `sqrt(r^2+h^2)`
= `sqrt(6^2+8^2) m`
= `sqrt100 m`
= 10 m
The curved surface area of conical tent = πrl
= (3.14 × 6 × 10) m2
= `314/100 xx 6 xx 10 m^2`
= 188.4 m2
Let the length of the tarpaulin sheet required be l.
As 20 cm will be wasted, therefore, the effective length will be (l − 0.2 m).
Breadth of tarpaulin = 3 m
Area of sheet = Curved surface area of the tent
[(l − 0.2 m) × 3] m = 188.4 m2
l − 0.2 m = 62.8 m
l = 63 m
Therefore, the length of the required tarpaulin sheet will be 63 m.
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