Question

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

(Use $\pi =3.14$)

• A. $63$ m
• B. $85$ m
• C. $74$ m
• D. $92$ m

Answer 1

Answer: (A)

$63$ m

Given,

$h=8m$, $r=6m$.

$\therefore$ Slant height $l=\sqrt{r^2+h^2}$

$=\sqrt{6^2+8^2}$ $=\sqrt{36+64}$

$=\sqrt{100}$ $=10$ m.

$\therefore$ Width surface area $=$ $\pi \left(r\right)\left(l\right)$

$=3.14\left(6\right)\left(10\right)$ $=1883.4m^2$.

Width of tarpaulin $=3$ m.

$\therefore$ length of tarpaulin $=\frac{188.4}{3}$ $=62.8$ m

Extra length of material required $=20$ cm $=0.2$ m

$\therefore$ actual length of tarpaulin required $=62.8$ m $+0.2$ m $=63$ m.

Hence, option $A$ is correct.