Question

The base of a conical tent is of area 616 sq.cm. A 48 cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given : area of base = 616 sq. cm
Height of conical tent = h = 48 cm
To find : total surface area of the conical tent.
Radius of the base = let r
Then, $\pi \times \left(r^2\right)=616sq.m\Rightarrow \left(r^2\right)=\left(\left(\frac{616}{\pi }\right)\right)=196sq.m\Rightarrow r=\sqrt{196}=14m$
Now, the total surface area of a cone is given by,
S =( Area of curved surface of cone + area of the base)
$=(\pi \times r\times l)+(\pi \times r\times r)=\pi \times r\times (l+r)$
where, l = the slant height of the cone
$I=\sqrt{\left\{\right(h{)}^2+\left(r{)}^2\right\}}=\sqrt{\left\{\right(48{)}^2+\left(14{)}^2\right\}}=\sqrt{(}2304+196)=\sqrt{2500}=50mSo,S=\pi \times (14)\times (50+14)=\pi \times (1464)=2816sq.m$