Total Surface Area of Cylinder

Total Surface Area of Cylinder

The total surface area (TSA) of a cylinder is the sum of its curved surface area and the area of its two circular bases. The curvedsurface area (CSA) of a cylinder is given by the product of its circumference of circular base (2πr) and the height (h) of the cylinder i.e. CSA = 2πrh. And the area of circular base is πr².

Hence, the total surface area of cylinder = Curved surface area + 2 × area of circular base

                                                                 = 2πrh + 2πr²

                                                                 = 2πr(h + r)

∴  Total surface area (TSA) of cylinder = 2πr(r + h)

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

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.

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

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

Since circumference (c) = 2πr, we can also write the formula of total surface area of cylinder as,

Total surface area (TSA) of cylinder = c(r + h)

Workout Examples

Example 1: Find the total 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,

                                Total surface area (TSA) = 2πr(r + h)

                                                                           = 2 × 22/7 × 7 (7 + 20)

                                                                           = 2 × 22 × 27

                                                                           = 1188cm²

                Thus, the total surface area of cylinder is 1188cm².

Example 2: The total surface area of a cylinder is 231 cm². Its CSA (curved surface area) is 2/3 of total surface area. Find the radius of its base and height.

Solution: Here,

                          Total surface area of the cylinder = 231cm²

                          Curved surface area = 2/3 of the total surface area of cylinder

                i.e.     2πrh = 2/3 × 231

                or,     2 × 22/7 × rh = 154

                or,     rh = 154 × 7/44

                or,     rh = 24.5 ………………… (i)

Again, Curved surface area = 2/3 of total surface area

                i.e.    2πrh = 2/3 × 2πr(r + h)

                or,     h = 2/3 × (r + h)

                or,     3h = 2r + 2h

                or,     h = 2r ………………….. (i)

From (i) and (ii),

                           r × 2r = 24.5

                or,      r² = 24.5/2

                or,      r² = 12.25

                or,      r = 3.5cm

From (ii),

                h = 2r = 2 × 3.5 = 7cm

                Thus, the radius is 3.5cm and height is 7cm.

Example 3: 50 circular plates, each of radius 7cm and thickness 0.5cm are placed one above the other to form a right circular cylinder. Find its total surface area.

Solution: Here,

                          Number of circular plates (N) = 50

                          Thickness of each plate = 0.5cm

                          ∴  Total height of cylinder (h) = 50 × 0.5cm = 25cm

                          Radius of each plate (r) = 7cm 

     

                Now,

                          The total surface area (TSA) of cylinder = 2πr(r + h)

                                                                                              = 2 × 22/7 × 7 × (7 + 25)

                                                                                              = 2 × 22 × 32

                                                                                              = 1408cm²

                Thus, the total surface area of cylinder is 1408cm².

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