Right Circular Cylinder

Rotate a rectangle ABCD about one of its edges say AB. The solid generated as a result of this rotation is called a right circular cylinder. In daily life, we come across many solids of this shape such as water pipes, tin cans, drums, powder boxes.

The two ends (or bases) of a right circular cylinder are congruent circles. A and B are the centres of these two circles of radii AD (= BC). Further, AB is perpendicular to each of these circles.

Here, AD (or BC) is called the base radius and AB is called the height of the cylinder. The surface formed by two circular ends are flat and the remaining surface is curved.

Surface Area

Take a hollow cylinder of radius r and height h and cut it along any line on its curved surface parallel to the line segment joining the centres of the two circular ends. You will obtain a rectangle of length 2πr and breadth h. Clearly, the area of this rectangle is equal to the area of the curved surface of the cylinder.

 So, curved surface area of the cylinder = area of the rectangle

= 2πr × h

= 2πrh

In case, the cylinder is closed at both the ends, then the total surface area of the cylinder

= 2πrh + 2πr²

= 2πr(r + h)

Volume

Volume of a right circular cylinder = Area of the base × height

= πr² × h

= πr²h