A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius of each is to the height of each as 3:4.

Explanation

To solve the problem, we need to show that the ratio of the radius (r) to the height (h) of both the cylinder and the cone is 3:4, given that their curved surface areas are in the ratio of 8:5.

### Step-by-Step Solution:

1. **Understand the Formulas for Curved Surface Area**:
- The curved surface area (CSA) of a cylinder is given by:
\[
\text{CSA}_{\text{cylinder}} = 2\pi rh
...