Question

What length of tarpaulin $3m$ wide will be required to make 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 $20cm$.

Answer 1

$h=8$m, $r=6$m, $l=\sqrt{r^2+h^2}$
$=\sqrt{6^2+8^2}$
$\sqrt{100}=10$m
CSA $=\pi rl=(3.14\times 6\times 10)m^2=188.4$m${}^2$
Let the length of sheet required $=x$
Breadth $=3$m
Area $=l\times b=3\times x=3x$
$20$cm of length will be wasted:
Effective length $=(x-\frac{20}{100})$
$=\frac{80}{100}x$m
CSA of tent $=$ Area of sheet
$188.4=\left(\frac{80x}{100}\right)3$
$\frac{80}{100}x=\frac{62.8}{10}m$, $l=\frac{628}{8}$m
$l=63$m