Explanation:

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

- Let's calculate the changes:

- Height: If the original height is $h$, the new height becomes $1.3h$ after a 30% increase.

- Radius: If the original radius is $r$, the new radius becomes $0.85r$ after a 15% decrease.

- Substituting the new values into the CSA formula:

- New CSA = $2\pi (0.85r)(1.3h)$.

- Simplify to find the change ratio:

- New CSA = $2\pi \times 0.85\times 1.3\times rh=2\pi \times 1.105\times rh$.

- Calculate percentage change:

- New CSA / Original CSA = 1.105.

- Percentage change = $(1.105-1)\times 100\mathrm{\%}=10.5\mathrm{\%}$.

Option 4: 10.5% is the correct answer.