Explanation:

- The formula for the curved surface area (CSA) of a cylinder is given by $2\pi rh$, where $r$ is the radius and $h$ is the height.

- Given: Height $h=21\text{cm}$ and CSA = $1386{\text{cm}}^2$.

- Substitute the given values into the CSA formula:

$$2\pi r\times 21=1386$$

- Simplify:

$$42\pi r=1386$$

- Solve for $r$:

$$r=\frac{1386}{42\pi }\approx 10.5\text{cm}$$

- Based on calculations, the radius is approximately 10.5 cm.

- Option 1, 10.5 cm, aligns with the calculation.