A right circular cylinder and a right circular cone have the same base radius 6 cm and the same height 8 cm. Find the ratio of the curved surface area of the cylinder to that of the cone.

Introduction / Context:Curved (lateral) surface area of a cylinder depends on radius and height; for a cone it depends on radius and slant height. With the same radius and height, we compute each and then form the ratio.

Given Data / Assumptions:

• Radius r = 6 cm; height h = 8 cm.
• CSA_cylinder = 2πrh.
• CSA_cone = πrl, where l = √(r^2 + h^2).

Concept / Approach:Compute l, then both CSAs, then the ratio.

Step-by-Step Solution:

Verification / Alternative check:Cancel π to simplify; ratio reduces cleanly to 8:5.

Why Other Options Are Wrong:Other ratios do not match the computed CSA values with l = 10.

Common Pitfalls:Using height instead of slant height in the cone’s CSA; forgetting to compute l by Pythagoras.

Final Answer:8 : 5