Question

A conical military tent having diameter of the base 24 m and slant height of the tent is 13 m, find the curved surface area of the cone. [π = 227]

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{Curved \ surface \ area \ of \ tent \ is \ 490.29 \ cm^{2}}$

$\sf\orange{Given:}$

$\sf{For \ conical \ military \ tent,}$

$\sf{\implies{Diameter (d)=24 \ m}}$

$\sf{\implies{Slant \ Height(l)=13 \ m}}$

$\sf\pink{To \ find:}$

$\sf{Curved \ surface \ area \ of \ the \ cone.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Radius(r)=\frac{Diameter}{2}}$

$\sf{Radius (r)=\frac{24}{2}=12 \ m}$

$\boxed{\sf{Curved \ surface \ area \ of \ cone=\pi\times \ r\times \ l}}$

$\sf{\therefore{Curved \ surface \ area \ of \ tent=\frac{22}{7}\times12\times13}}$

$\sf{\therefore{Curved \ surface \ area \ of \ tent=\frac{22\times12\times13}{7}}}$

$\sf{\therefore{Curved \ surface \ area \ of \ tent=\frac{3432}{7}}}$

$\sf{\therefore{Curved \ surface \ area \ of \ tent=490.29 \ cm^{2}}}$

$\sf\purple{\tt{\therefore{Curved \ surface \ area \ of \ tent \ is \ 490.29 \ cm^{2}}}}$

Answer 2

Given ,

Diameter of base of cone (d) = 24 m

Slant height of cone (l) = 13 m

So ,

Radius of base of cone (r) = 12 m

As we know that ,

The curved surface area of cone is given by

$\large \sf \underline{ \fbox{CSA \: of \: cone = \pi rl}}$

Thus ,

$</p><p>\sf \Rightarrow </p><p> </p><p>CSA = \frac{22}{7} \times 12 \times 13 \\ \\</p><p>\sf \Rightarrow </p><p> </p><p> CSA = \frac{3432}{7} \\ \\</p><p>\sf \Rightarrow </p><p> </p><p> CSA = 490.2 \: \: {m}^{2}$

$\therefore \bold{ \sf \underline{The \: curved \: surface \: area \: of \: cone \: is \: 490.2 \: \: {m}^{2} }}$