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.

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.

********************

10 Math Problems officially announces the release of Quick Math Solver and 10 Math Problems, Apps on Google Play Store for students around the world.

********************

********************

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.

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.