# Functional Skills: Surface Area

## Functional Skills: Surface Area Revision

**Calculating the Surface Area**

You may be given the area of each face of a 3D shape, or you will more likely be given the dimensions and have to work out the area of each face individually.

**Example:** Calculate the **surface area** of the cuboid.

The area of the front face and back face are both \textcolor{blue}{8} \times \textcolor{blue}{3} = 24 \text{ cm}^2

The area of the side faces are both \textcolor{blue}{5} \times \textcolor{blue}{3} = 15\text{ cm}^2

The area of the top face and bottom face are both \textcolor{blue}{8} \times \textcolor{blue}{5} = 40\text{ cm}^2

Therefore, the total surface area is

(2 \times 24) + (2 \times 15) + (2 \times 40) = 48 + 30 + 80 = 158 \text{ cm}^2

**Using Nets to find the Surface Area**

You can use **nets** to help find the surface area. This will help when calculating the surface area of all 3D shapes, especially prisms and cylinders.

**Example:** Calculate the **surface area** of the cylinder.

Give your answer to the nearest whole number.

Use \pi = 3.14

You can draw the net of this cylinder to help:

The net has two circles of radius \textcolor{red}{4} cm, and a rectangle of width \textcolor{blue}{5} cm and length which is equal to the circumference of the circles.

First, calculate the circumference of the circle:

circumference = \pi d = 2 \pi r = 2 \times 3.14 \times \textcolor{red}{4} = 25.12 cm

Then, calculate the areas of the faces:

area of rectangle = 25.12 \times \textcolor{blue}{5} = 125.6 cm^2

area of circle =\pi r^2 = 3.14 \times \textcolor{red}{4}^2 = 50.24 cm^2

So, add the areas of all the faces together, to find the surface area of the cylinder:

surface area of cylinder = 50.24 + 50.24 + 125.6 = 226.08 = 226 cm^2

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**Example: Surface Area of a Pyramid**

Calculate the surface area of the pyramid.

**[4 marks]**

All 4 triangular faces are equal.

So, we can calculate the area of one triangle and multiply it by 4 to get the area of all of them.

Area of triangle = \dfrac{1}{2} \times b \times h = \dfrac{1}{2}\times5\times8=20 cm^2

Therefore, the area of all 4 triangles is

4\times20=80 cm^2

Now, we need to find the area of the square base,

Area of base =5 \times 5=25 cm^2

Therefore, the surface area is the area of each face added together:

Total surface area =25+80=105 cm^2

## Functional Skills: Surface Area Example Questions

**Question 1:** A cube has sides of length 7 cm.

Calculate the surface area of the cube.

**[2 marks]**

The area of one square face is

7 \times 7 = 49 cm^2

Therefore, since a cube has 6 square faces, the surface area is

6 \times 49 = 294 cm^2

**Question 2:** Below is a cuboid with length 6 mm, width 2.5 mm, and height 4 mm.

Calculate the surface area of the cuboid.

**[3 marks]**

Area of front face:

4\times2.5=10 mm^2

Therefore, the back face also has area 10 mm^2

Area of right side face:

6\times4=24 mm^2

Therefore, the left side face also has area 24 mm^2

Area of top face:

6\times2.5=15 mm^2

Therefore, the bottom face also has area 15 mm^2

Total surface area:

10+10+24+24+15+15=98 mm^2

**Question 3:** Calculate the surface area of the prism in the diagram below.

**[4 marks]**

The area of the front triangular face is

\dfrac{1}{2} \times 6 \times 4 = 12 cm^2

The area of the back triangular face is therefore 12 cm^2 also.

The area of a slanted rectangular face is

11 \times 5 = 55 cm^2

The area of the other slanted rectangular face is also 55 cm^2

The area of the rectangular base is

11 \times 6 = 66 cm^2

Therefore, the total surface area is

12 + 12 + 55 + 55 + 66 = 200 cm^2

## Functional Skills: Surface Area Worksheet and Example Questions

### Surface Area L2

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