Question

What length of tarpaulin $3m$ wide will be required to make a conical tent of height $8m$ 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 = $8m$
Radius ($r$) of base of the tent = $6m$
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 $20cm$ will be wasted, the effective length will be ($l-0.2)m$.
Breadth of tarpaulin = $3m$
Area of sheet = CSA of the tent
$\left[\right(l-0.2)\times 3]m^2=188.4m^2$ [Area of rectangular sheet = $l\times b$]
($l-0.2)m$ = $62.8m$
$l=63m$

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