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

Given parameters of the conical tent:
* Base radius, $r=21\text{m}$
* Height, $h=28\text{m}$

Step 1: Calculate the slant height ($l$) of the cone using Pythagoras' theorem:

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

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

Step 2: Find the Curved Surface Area ($\text{CSA}$) of the cone, which represents the total area of the cloth required:

$$\text{CSA}=\pi rl$$

$$\text{CSA}=\frac{22}{7}\times 21\times 35$$

$$\text{CSA}=22\times 3\times 35=2310{\text{m}}^2$$

Step 3: Find the required length of the cloth. Since the cloth is rectangular:

$$\text{Area of cloth}=\text{Length}\times \text{Width}$$

$$2310=\text{Length}\times 5$$

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

Therefore, $462\text{ meters}$ of cloth will be required.