Question

a conical tent has radius 7 metre and height is 24 metre find the length of 10 wide tarpaulincloth required to make it​

Answer 1

Step-by-step explanation:

Given:

Radius of conical tent is, r=7\ mr=7 m

Height of conical tent is, h=24\ mh=24 m

Width of tarpaulin is, b=10\ mb=10 m

Let the length of tarpaulin be ll m.

Volume of air inside a conical tent will be equal to volume of the conical tent. As the tent is conical in shape, therefore the volume is equal to the volume of a cone. Therefore,

Volume of air inside the tent is given as:

\begin{lgathered}V=\frac{1}{3}\times \pi\times r^2\times h\\\\V=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24\\\\V=22\times 7\times 8=1232\ m^3\end{lgathered}

V= 3

1

×π×r

2

×h

V=

3

1

×

7

22

×7

2

×24

V=22×7×8=1232 m

3

Therefore, the volume of the sir inside the tent is 1232 m³.

Now, area of tarpaulin cloth required is equal to the surface area of the conical tent which is given as:

\begin{lgathered}SA=\pi\times r\times \sqrt{(r^2+h^2)}\\\\SA=\frac{22}{7}\times 7\times \sqrt{7^2+24^2}\\\\SA=22\times 25\\\\SA =550\ m^2\end{lgathered}

SA=π×r×

(r

2

+h

2

)

SA=

7

22

×7×

7

2

+24

2

SA=22×25

SA=550 m

2

Now, area of tarpaulin is equal to the product of its length and width.

Therefore, area of tarpaulin is given as:

\begin{lgathered}l\times b=550\\\\l\times 10=550\\\\l=\frac{550}{10}=55\ m\end{lgathered}

l×b=550

l×10=550

l=

10

550

=55 m

So, the length of tarpaulin required is 55 m.