Answer:
radius : height = 7 : 3
Explanation:
You want the ratio of the base radius to the height of a cylinder that has 30% of its surface area as lateral area.
Lateral area
The lateral area of a cylinder is ...
LA = 2πrh
Base area
The base area of a cylinder is ...
A = 2(πr²) = 2πr·r
Ratio
Then the ratio of lateral area to total area is ...

Inverting this relation lets us solve for r/h:
