Total Surface Area of Cylinder

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.

Total surface area of cylinder = Curved surface area + 2 × area of circular base

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)
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.
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.

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