In this activity we will calculate the surface areas of cylinders.

Here is a cylinder. (It is very similar to a prism with a circular cross-section)

To find the surface area of this 3D shape we have see what the net looks like!

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

To calculate the surface area, we need the **area of the circle x 2 + area of rectangle**

**Area of circle**

**The area of a circle is πr ^{2 }**

**Area of Rectangle**

Area = height x the **circumference** of a circle

Area = **π x diameter x height**

**Area = ** **πd x H**

**Surface Area of a Cylinder**

So the surface area is the area of the two circles + 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**

Let's look at a typical question!

__Example__

Find the surface area of this cylinder in cm^{2} to 1 decimal place.

**Answer**

Diameter = 6 cm

Radius = 6 ÷ 2 = 3 cm

Height = 12 cm

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

SA = 2 x π x 3^{2} + 2 x π x 3 x 12

SA = 282.74

SA = **282.7 cm ^{2 }**(1 dp)

Let's do some questions!