Question

What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately $20cm.[Use\pi =3.14]$

Answer 1

Height (h) of the conical tent = 8 m
Radius (r) of base of the tent= 6 m
Slant height (l) of the tent $=\sqrt{r^2+h^2}$
$=\left(\sqrt{6^2+8^2}\right)m=\left(\sqrt{100}\right)m=10m$
CSA of conical tent = $\pi rl$
$=(3.14\times 6\times 10)m^2$
$=188.4m^2$
Let the length of tarpaulin sheet required be l.
As 20 cm=0.2 m will be wasted, so the effective length will be ( l – 0.2 m).
Breadth of tarpaulin = 3 m
Area of sheet = CSA of the tent
$\left[\right(l-0.2)\times 3]m^2=188.4m^2$
l – 0.2 m = 62.8 m
l = 63 m
therefore, the length of the required tarpaulin sheet will be 63 m.