Question

The length of canvas $1.1$ m wide required to build a conical tent of height $14$ m and the floor area $346.5m^2$, is:

• A. $65$ m
• B. $525$ m
• C. $490$ m
• D. $860$ m

Answer 1

The correct option is B $525$ m

Given, $h=14$ m and floor area $=346.5$ $m^2$.

We know, the base of a cone is a circle.
Then, $\Rightarrow \pi r^2=346.5$

$\Rightarrow r^2=346.5\times \frac{7}{22}=110.25\Rightarrow r=10.5$.

$\therefore$ Slant height, $l=\sqrt{r^2+h^2}=\sqrt{{\left(10.5\right)}^2+{\left(14\right)}^2}=\sqrt{110.25+196}$
$=\sqrt{306.25}=17.5$ m.

$\therefore$ Curved surface area $=\pi rl$
$=\frac{22}{7}\times 10.5\times 17.5=\frac{4042.5}{7}{m}^2$.

Width of cloth $=1.1$ m.

$\therefore$ Length of cloth required $=\frac{\left(\frac{4042.5}{7}\right)}{1.1}=\frac{4042.5}{7.7}=525m.$

Hence, $525$ m length of canvas is required to build the conical tent.

Therefore, option $B$ is correct.