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Chapter Overview
Learning Goals
Learning Goals
Maths
Summary
The surface area of a shape is the sum of the areas of its faces. The surface area of 3D shapes can either be calculated using nets or using given formulae.
A net is a 3D shape that has been unfolded and laid out flat. Here are some examples of nets.
SHAPE | NET |
| |
| |
| |
To find the surface area of a shape using nets, sketch the net and work out the area of the net. This can be done by working out the area of each individual shape in the net.
What is the surface area of a cube with side lengths $8cm$?
First, sketch the net:
The net of a cube is six squares. In this example, each square will have side lengths $8cm$.
Then, find the area of the net:
The net is a compound shape consisting of six squares.
The area of one of these squares is given to be:
$8\times8=64cm^2$
The area of the net is therefore:
$6\times64=384cm^2$
The surface area of the cube is $\underline{384 \ cm^2}$.
These are the formulae you need to know:
SHAPE | FORMULA | DIAGRAM |
Sphere | $S.A=4\pi r^2$ | |
Cylinder | $S.A=2\pi r^2 +2\pi rh$ | |
Cone | $\text{Curved surface area}=\pi rl$ $S.A=\pi rl +\pi r^2$ | |
What is the surface area of a sphere with radius $2m$ to three significant figures?
Substitute $r=2$ into the formula:
$\begin{aligned}S.A&=4\pi r^2\\&=4\pi (2)^2\\&=16\pi\\&=50.26548246...m^2\end{aligned}$
The surface area is $\underline{50.3m^2\space\ (3\space s.f.)}$.
The surface area of a shape is the sum of the areas of its faces. The surface area of 3D shapes can either be calculated using nets or using given formulae.
A net is a 3D shape that has been unfolded and laid out flat. Here are some examples of nets.
SHAPE | NET |
| |
| |
| |
To find the surface area of a shape using nets, sketch the net and work out the area of the net. This can be done by working out the area of each individual shape in the net.
What is the surface area of a cube with side lengths $8cm$?
First, sketch the net:
The net of a cube is six squares. In this example, each square will have side lengths $8cm$.
Then, find the area of the net:
The net is a compound shape consisting of six squares.
The area of one of these squares is given to be:
$8\times8=64cm^2$
The area of the net is therefore:
$6\times64=384cm^2$
The surface area of the cube is $\underline{384 \ cm^2}$.
These are the formulae you need to know:
SHAPE | FORMULA | DIAGRAM |
Sphere | $S.A=4\pi r^2$ | |
Cylinder | $S.A=2\pi r^2 +2\pi rh$ | |
Cone | $\text{Curved surface area}=\pi rl$ $S.A=\pi rl +\pi r^2$ | |
What is the surface area of a sphere with radius $2m$ to three significant figures?
Substitute $r=2$ into the formula:
$\begin{aligned}S.A&=4\pi r^2\\&=4\pi (2)^2\\&=16\pi\\&=50.26548246...m^2\end{aligned}$
The surface area is $\underline{50.3m^2\space\ (3\space s.f.)}$.
Nets and surface area
FAQs
Question: Which shapes have a formula to work out their surface area?
Answer: There are given formulae to work out the surface area of a sphere, a cylinder and a cone.
Question: How do you work out the surface area of a shape using nets?
Answer: First, sketch the net. Then, work out the area of the net by working out the area of each individual shape in the net.
Question: What are the two ways of working out surface area?
Answer: The two ways of finding the surface area of a shape is to use a net or to use a formula.
Theory
Exercises
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