The curved surface area of a cone is $308\text{cm}{2}^{}$, and its slant height is $28\text{cm}$. Find the radius of its base. (Use $\pi =\frac{22}{7}$)

The correct answer is 3.5 cm.

To find the radius of the base of the cone, we can use the formula for the curved surface area (CSA) of a cone:
$\text{Curved Surface Area (CSA)}=\pi rl$
where:
- $r$ is the radius of the base of the cone,
- $l$ is the slant height of the cone.

From the given information:
- Curved Surface Area (CSA) = $308{\text{cm}}^2$
- Slant height ($l$) = $28\text{cm}$
- $\pi =\frac{22}{7}$

Substitute these values into the formula:
$308=\frac{22}{7}\times r\times 28$

Simplify the equation:
$308=22\times r\times 4$
$308=88\times r$

Now, solve for $r$:
$r=\frac{308}{88}$
$r=3.5\text{cm}$

Thus, the radius of the base of the cone is 3.5 cm.