Look at this cylinder.

Its net is made up of two circles and a rectangle.

In the two formulae below, r is the radius and d is the diameter.

The **area **of a circle is** πr ^{2 }**

The **circumference** of a circle is **πd**

Look at these diagrams to see that the base of the rectangle has the same length as the circumference of the circle.

So the surface area is the area of the two circles plus the area of the rectangle.

The area of the two circles = 2πr^{2}

The area of the rectangle = πdh or we can write 2πrh (because the diameter is the radius x 2)

**Surface Area** = 2πr^{2} + πdh = **2πr ^{2} + 2πrh**

**Example**

Find the surface area of this cylinder in cm^{2} to 3 significant figures.

**Answer**

Diameter = 6 cm

Radius = 6 ÷ 2 = 3 cm

Height = 12 cm

**Surface Area** = **2πr ^{2} + 2πrh** = 2 x π x 3

^{2}+ 2 x π x 3 x 12 = 282.74 ≈

**283 cm**(3 s.f.)

^{2 }

Let's get started.