Question

The total surface area of a conical tent is $920$ square meter and its radius $14$ m. Find the slant height. (Round off your answer to the nearest whole number).

• A. $7$ m
• B. $6$ m
• C. $5$ m
• D. $6.5$ m

Answer 1

The correct option is A $7$ m

We know, the total surface area of cone$=\pi rs+\pi r^2$,

where $r$ is the radius of the base of the cone and $s$ is the slant height.

Given, the total surface area of cone$=920m^2$ and $r=14m$.

Let, $\pi =3.14$.

Substituting the values in the formula we get,

$\Rightarrow 940=3.14\times 14s+3.14\times {14}^2$

$\Rightarrow 940=43.96\times s+3.14\times 196$

$\Rightarrow 940=43.96\times s+615.44$

$\Rightarrow 940-615.44=43.96\times s$

$\Rightarrow 324.56=43.96\times s$

$\Rightarrow s=\frac{324.56}{43.96}$

$\Rightarrow s=7.38\approx 7m$.

Therefore, option $A$ is correct.