The curved surface area of a cylinder is half of its total surface area. If its height is 102 cm, then find its radius (in cm).

Correct option is D

Given:

- The curved surface area (CSA) is half of the total surface area (TSA).
- The height of the cylinder is 102 cm.
- We need to find the radius of the cylinder.
Formula Used:
Curved Surface Area (CSA) of a cylinder = 2πrh
Total Surface Area (TSA) of a cylinder = 2πr(r + h) 

Solution:
: Relationship between CSA and TSA
According to the given condition:
CSA = (1/2) × TSA
2πrh = (1/2) × 2πr(r + h)
h = (1/2) × (r + h)
2h = r + h
r = 2h - h = h
We are given that the height h = 102 cm, so:
r = 102 cm
The radius of the cylinder is 102 cm. 

​The curved surface area of a cylinder is half of its total surface area. If its height is 102 cm, then find its radius (in cm).​