Functional Skills: Surface Area

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Functional Skills: Surface Area Revision

Surface Area of 3D Shapes

The surface area of any 3D shape is the areas of all faces of the shape added together. You can use nets to help find the surface area.

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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 cm^2

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

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

Therefore, the total surface area is

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

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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

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Functional Skills: Surface Area Example Questions

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

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

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

Additional Resources

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