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  • 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.

Q : 5    What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and a base radius of 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 \small \pi =3.14).
 

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Given,

base radius of the conical tent = r =6\ m

height of the tent = h =8\ m

We know,

curved surface area of a cone = \pi rl = \pi r\sqrt{h^2 + r^2}

\therefore Area of tarpaulin required = Curved surface area of the tent

\\ =3.14\times6\times \sqrt{8^2+ 6^2} \\ = 3.14\times6\times 10 \\ = 188.4\ m^2

Now, let the length of the tarpaulin sheet be x\ m

Since 20\ cm is wasted, effective length = x - 20 cm = (x - 0.2)\ m

Breadth of tarpaulin = 3\ m

 \\ \therefore [(x - 0.2) \times 3] = 188.4 \\ \Rightarrow x - 0.2 = 62.8 \\ \Rightarrow x = 63\ m

Therefore, the length of the required tarpaulin sheet will be 63 m.

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Nehul

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