Total surface area of a cylinder is the sum the surface area of each end and the surface area of the sides of the cylinder. The total surface area (TSA) includes the area of the circular top and base, as well as the curved surface area (CSA) of the cylinder.

TSA = Area of the lid + Area of the base + Curved surface area

= $\pi r^2$ + $\pi r^2$ + 2$\pi$ rh

= 2$\pi r^2$ + 2$\pi$ rh

= 2$\pi$r(r + h)

**Formula:**

Total Surface Area of a Cylinder = 2 $\pi$ r(r + h).

Where, **r** is radius and **h **is height of a cylinder.**Example:**Find the total surface area of a cylindrical tin of radius 6 cm and height 9 cm.

**Solution:**

Step 1:

Radius of a cylinder = 6 cm

Height of a cylinder = 9 cm

Step 2:Total surface area of a cylinder (TSA) = 2 $\pi$ r (r + h)=> TSA = 2 *

$\frac{22}{7}$ * 6(6 + 9)

= 12 *

$\frac{22}{7}$ (15)

= 565.71

Hence the total surface area of a cylinder is 565.71 cm

^{2} .