Question

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

Answer 1

Curved surface area of tent $=\pi rl$

$r=6m,h=8m$

We know that

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

$l=\sqrt{100}$

$l=10m$

Curved surface area of tent $=3.14\times 6\times 10$

$=188.4m^2$

Now,

Area of tarpaulin material $=$ Area of tent

$L\times B=188.4$

$L\times 3=188.4$

$L=\frac{188.4}{3}$

$L=62.8m$

Now, given that margin is 20 cm

Total length $=$ Length $+$ Margin

$=62.8+20\times \frac{1}{100}$

$=62.8+0.2$

$=63m$