Surface area of a cylinder

Objective:

  1. To determine the area of a given cylinder.
  2. To obtain the formula for the lateral surface area of a right circular cylinder in terms of the radius(r) of its base and height (h).

Theory:

Right circular cylinder:

Definition: A right circular cylinder is a three-dimensional object with two congruent circles as parallel bases and a lateral surface consisting of a rectangle.

Base and side: The bases of right circular cylinder are always congruent and parallel to each other. If you were to 'unroll' the cylinder you would find the side is actually a rectangle when flattened out.

Height: The height h is the perpendicular distance between the bases.

Radius: The radius r of a cylinder is the radius of a base.

Surface area of a cylinder :

To find the surface area of a cylinder add curved (lateral) surface area and area of both bases.

Area of both bases - Each base is a circle so the area of each base is πr², where r is the radius of the base. There are two bases so their combined surface area is 2 X πr².

Curved Surface Area - As mentioned above the surface area of the cylinder opens to form a rectangular region. Breadth of this rectangle in height of the cylinder i.e h and Length of the rectangle is circumference of the base of the cylinder i.e. 2πr. Hence area of curved surface area - 2πr X h

Total surface area of cylinder = curved surface area (c) + 2 (area of base circle)

                                                     = 2.π.r.h + 2.π.r²

                                                     = 2.π.r (h + r)

 

Cite this Simulator: