Answer: The formula for the surface area of a cylinder is given by 2πr(h + r), where r is the radius and h is the height.
In this case, h = 10 cm and CSA = 500 cm². We can use this information to find the radius of the cylinder:
CSA = 2πr(h + r)
500 = 2πr(10 + r)
Expanding and rearranging:
500 = 20πr + 2πr^2
2πr^2 + 20πr - 500 = 0
We can use the quadratic formula to solve for r:
r = (-b ± √(b^2 - 4ac)) / 2a
where a = 2π, b = 20π, and c = -500.
Plugging in the values:
r = (-20π ± √(20π^2 - 4 * 2π * -500)) / 2 * 2π
r = (-20π ± √(400π^2 + 2000π)) / 4π
r = (-20π ± √(400π^2 + 2000π)) / 4π
r = (-20/π ± √(400 + 2000/π)) / 4
The radius of the cylinder is approximately 3.56 cm.
Explanation: