What length of tarpaulin 4 m wide will be required to make a conical tent of height 8 m and base radius 6 m?
Question:

What length of tarpaulin 4 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assume that the extra length of material will be required for stitching margins and wastage in cutting is approximately 20 cm.

 

Solution:

Given that,

Height of conical tent (h) = 8 m

Radius of base of tent (r) = 6 m

Slant height (l)

(l) $=\sqrt{\mathrm{r}^{2}+\mathrm{h}^{2}}$

$=\sqrt{8^{2}+6^{2}}$

$=\sqrt{100}=\sqrt{10} \mathrm{~m}$

C.S.A of conical tent $=\pi r \mid$

$=(3.14 * 6 * 10) \mathrm{m}^{2}=188.4 \mathrm{~m}^{2}$

Let the length of tarpaulin sheet required be l

As 20 cm will wasted, so effective

Length will be (l – 0.2 m)

Breadth of tarpaulin = 3m

Area of sheet = C.S.A of sheet

$[1 * 0.2 * 3] \mathrm{m}=188.4 \mathrm{~m}^{2}=1-0.2 \mathrm{~m}=62.8 \mathrm{~m}$

Accounting extra for wastage:

⟹ l = 63 m

Thus the length of the tarpaulin sheet will be = 63 m

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