Question

The base of a conical tent is of area 616 sq units. A vertical pole of length of 48 units is placed at its centre so that it touches the roof of the tent. How much canvas (in sq
$\text{units)is needed to make the tent if the base is also covered with canvas? [Take}\pi =\frac{2}{7}]$

Answer 1

Here, we need to calculate the total surface area of the cone.

We know:
$\text{Total surface area of the cone}=\pi r(l+r)$
$=\pi rl+\pi r^2$
$\text{where}\pi r^2\text{is the area of the base of}$
$\text{the cone and}l\text{is the slant height}$
$\text{of the cone}.$

Given:
Area of base = 616 sq units


$\pi r^2=616\text{sq units}$
$\Rightarrow \frac{22}{7}\times r^2=616$

$\Rightarrow r^2=616\times \frac{7}{22}=196$
$\Rightarrow r=\sqrt{196}\text{unit}$
$\Rightarrow r=14\text{unit}$

Also, height of cone = 48 units


We know:
$L=\sqrt{h^2+r^2}$
$=\sqrt{{48}^2+{14}^2}$
$=\sqrt{2304+196}$
$=\sqrt{2500}=50\text{units}$

$\text{Total surface area of a cone}=\pi rl+\pi r^2$

So, total surface area of the conical tent $=\pi rl+\pi r^2$

$=\frac{22}{7}\times 14\times 50+616$

$=2816\text{sq units}$