Final answer:
The ratio of the curved surface area to the total surface area provided is not possible, so there is no valid radius for the base of the cylinder.
Step-by-step explanation:
To find the radius of the base of the cylinder, we need to determine the radius of the solid hemisphere first. The ratio of the curved surface area to the total surface area of the hemisphere can help us find this radius. Let's set up the equation:
Curved Surface Area of Hemisphere / Total Surface Area of Hemisphere = 2 / 5
The curved surface area of a hemisphere is given by 2πr², and the total surface area is given by 3πr². Substituting these values into the equation, we get:
2πr² / 3πr² = 2 / 5
Simplifying this equation, we get:
r² / r² = 2 / 5
1 = 2 / 5
5 = 2
This equation is not true, which means that the given ratio of the curved surface area to the total surface area is not possible. Therefore, there is no valid radius for the base of the cylinder in this case.