How many metres of cloth will be required to make a conical tent, the radius of whose base is $21\text{metres}$ and height is $28\text{metres}$, if the width of the cloth is $5\text{metres}$? (Where $\pi =\frac{22}{7}$)

To find the amount of cloth required for a conical tent, we need to find its curved surface area ($\text{CSA}$).
Given:

* Radius ($r$) = $21\text{m}$
* Height ($h$) = $28\text{m}$

First, calculate the slant height ($l$) of the cone using Pythagoras' theorem:

$$l=\sqrt{r^2+h^2}$$

$$l=\sqrt{21^2+28^2}=\sqrt{441+784}=\sqrt{1225}=35\text{m}$$

Now, find the curved surface area ($\text{CSA}$):

$$\text{CSA}=\pi rl=\frac{22}{7}\times 21\times 35=22\times 3\times 35=2310{\text{m}}^2$$

The area of the cloth required is equal to the curved surface area of the tent. Since the cloth is rectangular:

$$\text{Area of cloth}=\text{Length}\times \text{Width}=2310{\text{m}}^2$$

Given the width of the cloth is $5\text{metres}$:

$$\text{Length}=\frac{2310}{5}=462\text{metres}$$