How is the surface area of a right circular cylinder calculated?

The surface area of a right circular cylinder is calculated by considering both the lateral area and the area of the two circular bases. The formula involves two components:

1. The area of the circular bases: Each base has an area of (πr^2), and since there are two bases, the total area contributed by the bases is (2πr^2).

2. The lateral surface area: The lateral area of the cylinder can be visualized as a rectangle that wraps around the sides of the cylinder. The height of this rectangle is the height of the cylinder (h), and the width is the circumference of the base, which is (2πr). Thus, the lateral surface area is (2πrh).

Combining these two components gives the total surface area formula:

S.A. = (2πr^2 + 2πrh).

This formula accurately represents the total surface area of a right circular cylinder, including both its lateral surface and the two circular ends. Thus, the correct choice encompasses all necessary measurements for calculating the complete surface area of the cylinder.