Explanation:

- The curved surface area (CSA) of a cylinder is given by the formula: $2\pi rh=19.5{\text{m}}^2$.

- The volume (V) of a cylinder is given by: $\pi r^{2}h=39{\text{m}}^3$.

- From the CSA formula, you have $h=\frac{19.5}{2\pi r}$.

- Substitute the value of $h$ from CSA into the volume formula: $\pi r^2\left(\frac{19.5}{2\pi r}\right)=39$.

- Simplify and solve for $r$: $r\cdot 19.5=78$.

- This gives $r=\frac{78}{19.5}=4$.

- Correct Answer: 4