Curved Surface Area of Cylinder

Curved Surface Area of Cylinder

Curved Surface Area of Cylinder

The total area around the curved part of a cylinder is called the curved surface area (CSA) of the cylinder. The curved surface area (CSA) of a cylinder is given by the product of its circumference of circular base (2πr) and height (h) of the cylinder i.e. CSA = 2πrh

This formula can be understood and derived by the following activities.

CSA of Cylinder = Area of rectangle ABCD

Let, the cylinder be hollow and made up of thin sheet of paper (or metal). If we cut the curved surface along the height AB and unfold it, then the thin sheet takes the shape of a rectangle ABCD.

The segment DC is coincident with the segment AB when the sheet was not unfolded. The length of AB = h, the height of the cylinder. The length of AD = circumference of the upper circular end = 2πr.

Hence, the curved surface area (CSA) of the cylinder = area of the rectangle ABCD
                                                                                     = AD × AB
                                                                                     = 2πr × h
                                                                                     = 2πrh

  Curved surface area (CSA) of a cylinder = 2πrh


Workout Examples

Example 1: Find the curved surface area of the given cylinder.
Cylinder

Solution: Here,
                          Diameter of the cylinder (d) = 14cm
                            Radius of the cylinder (r) = 14cm/2 = 7cm
                          Height of the cylinder (h) = 20cm

                We know,
                                Curved surface area (CSA) = 2πrh
                                                                              = 2 × 22/7 ×7 ×20
                                                                              = 880cm2

                Thus, the curved surface area of cylinder is 880cm2.


Example 2: The height of a cylinder is 15cm. The curved surface area is 660cm2. Find the radius of the base.

Solution: Here,
                          Height of the cylinder (h) = 15cm
                          Radius (r) = ?

                          Curved surface area (CSA) = 660cm2
                i.e.     2πrh = 660
                or,      2 × 22/7 × r × 15 = 660
                or,      660/7 × r = 660
                or,      r = 660 × 7/660
                or,      r = 7cm

                Thus, the radius of the base is 7cm.


Example 3: The curved surface area of a right circular cylinder is 4400cm2 and the circumference of its base is 110cm. Find the height of the cylinder.

Solution: Here,
                          Circumference of the cylinder = 110cm
                i.e.     2πr = 110cm.
      
                          Curved surface area  of the cylinder = 4400cm2
                i.e.     2πrh = 4400
                or,     110h = 4400
                or,     h = 4400/110
                or,     h = 40cm

                Thus, the height of the cylinder is 40cm.


You can comment your questions or problems regarding the CSA of cylinder here.

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