The surface area of a cylinder of radius r and height h is equivalent to which of the following expressions?

A cylinder can be divided into three parts - two circles and a rectangle as:

The surface area of a cylinder is the sum of the areas of the circles and the rectangle.

The length of the rectangle is the height of the cylinder, i.e., h. The width of the rectangle is equivalent to the circumference of the circular bases, i.e., 2πr.

Thus, area of the rectangle = length × width = h × 2πr = 2πrh

Note that this is also called the lateral surface area of a cylinder because it does not include the area of the circular bases.

Now, the two circular bases have a radius of 'r' each.

Thus, area of each circular base = π × r² = πr²

Thus, the surface area of the cylinder = area of the rectangle + area of two circles

= 2πrh + 2 × πr²

= 2πr (h + r)

Therefore, the surface area of the cylinder must be expressed by 2πr (h + r).