Height 'h' of a cylinder equals the circumference of its base. Then, the curved surface area in terms of 'h' is:

The height h of a cylinder is equal to the circumference of its base.

Circumference of the base:

h = 2πr

Curved surface area (CSA) of the cylinder:

CSA = 2πrh

Let the radius of the base of the cylinder be r.

Now,

h = 2πr

r = $$\frac{h}{2 \pi} ​$$​​

Substituting $$r = \frac{h}{2 \pi}$$​ into the formula for CSA:

​$$\text{CSA} = 2 \pi \left(\frac{h}{2 \pi}\right) h$$​​

​$$\text{CSA} = h \cdot h = h^2$$​​
Thus, The curved surface area of the cylinder in terms of h is $$\bf h^2.$$​​