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Cube
A Are all the faces the same? YES

4m How many faces are there?
6

Find the Surface area of one of
the faces.

4 x 4 = 16 Take that times the
number of faces.
X6
96 m2
SA for a cube.

Surface Area
 What does it mean to you?
 Does it have anything to do with what is in the inside
of the prism.?
 Surface area is found by finding the area of all the
sides and then adding those answers up.
 How will the answer be labeled?
 Units2 because it is area!

Triangular Prism
How many faces are
4 5 there? 5
How many of each shape does it take to
make this prism?
10 m
3
2 triangles and 3 rectangles = SA of a triangular prism

Find the surface area. Start by finding
the area of the triangle.
4 x 3/2 = 6 x 2= 12
How many triangles were there? 5 x 10 = 50 = front
2
4 x 10 = 40 = back
Find the area of the 3 3 x 10 = 30 = bottom
rectangles.

What is the final SA? SA = 132 m2

SA
 You can find the SA of any prism by using the basic
formula for SA which is
 2B + LSA= SA
 LSA= lateral Surface area
 LSA= perimeter of the base x height of the prism
 B = the base of the prism.

Triangular Prisms
 Use the same triangular prism we used
before. Let’s us the formula this time. 2B +
LSA=SA
 Find the area of the base, which is a triangle
because it is a triangular prism. You will need
two of them.
 Now, find the perimeter of that same base and
multiply it by how many layer of triangles are
in the picture. That is the LSA.
 Add that to the two bases. Now you should
have the same answer as before.
 Either way is the correct way.

Cylinders
What does it take to make this?
6
10m
2 circles and 1 rectangle= a cylinder
2B + LSA = SA

2B 3.14 x 9 = 28.26 X 2 = 56.52

+ LSA(p x H) 3.14 x 6 =18.84 x 10 = 188.4

SA = 244.9
2

 Why should you learn about surface area?
 Is it something that you will ever use in everyday
life?
 If so, who do you know that uses it?
 Have you ever had to use it outside of math?

Surface Area

 Triangular prism – a prism with two parallel,
equal triangles on opposite sides.

To find the surface
area of a triangular
h w prism we can add
l up the areas of the
separate faces.

Surface Area
 In a triangular prism there are two pairs of
opposite and equal triangles.

We can find the surface area of this
prism by adding the areas of the pink
8 cm side (A), the orange sides (B), the green
A bottom (C) and the two ends (D).

2 cm B C 5 cm
7 cm

Surface Area
 We should use a table to tabulate the various
areas.

Example:
Side Area Number Total
of Sides Area
8 cm
A
A

2 cm B C 5 cm B
7 cm C
D
Total

Surface Area
areas.

Example:
of Sides Area
8 cm
A
A 40 cm2 1 40 cm2

2 cm B C 5 cm B
7 cm C
D
Total

Surface Area
areas.

Example:
of Sides Area
8 cm
A
A 40 cm2 1 40 cm2

2 cm B C 5 cm B 10 cm2 1 10 cm2
7 cm C
D
Total

Surface Area
areas.

Example:
of Sides Area
8 cm
A
A 40 cm2 1 40 cm2

2 cm B C 5 cm B 10 cm2 1 10 cm2
7 cm C 35 cm2 1 35 cm2
D
Total

Surface Area
areas.

Example:
of Sides Area
8 cm
A
A 40 cm2 1 40 cm2

2 cm B C
D 5 cm B 10 cm2 1 10 cm2
7 cm C 35 cm2 1 35 cm2
D 7 cm2 2 14 cm2
Total

Surface Area
areas.

Example:
of Sides Area
8 cm
A
A 40 cm2 1 40 cm2

2 cm B C
D 5 cm B 10 cm2 1 10 cm2
7 cm C 35 cm2 1 35 cm2
D 7 cm2 2 14 cm2
Total 5 99 cm2

Example:
Surface Area
 Now you try...find the surface area!
B

Side Area No of Area
Sides

C

Example:
Surface Area
 Now you try...find the surface area!
B

Side Area No of Area
Sides
2.1m
C

2.0m
11.0m

2.0m

Shape and Space

Cuboids

Surface area of a cuboid

To find the surface area of a shape, we calculate the total area of all of the
faces.

A cuboid has 6 faces.

The top and the bottom of the cuboid have
the same area.


faces.


The front and the back of the cuboid have
the same area.


faces.


The left hand side and the right hand side
of the cuboid have the same area.


faces.

Can you work out the surface area of
5 cm this cuboid?
8 cm

The area of the top = 8 × 5
= 40 cm2

7 cm The area of the front = 7 × 5
= 35 cm2

The area of the side = 7 × 8
= 56 cm2


faces.

5 cm So the total surface area =
8 cm

2 × 40 cm2 Top and bottom

7 cm + 2 × 35 cm2 Front and back

+ 2 × 56 cm2 Left and right side

= 80 + 70 + 112 = 262 cm2

Formula for the surface area of a cuboid

We can find the formula for the surface area of a cuboid as follows.

Surface area of a cuboid =
w
l
2 × lw Top and bottom

+ 2 × hw Front and back
h

+ 2 × lh Left and right side

= 2lw + 2hw + 2lh

Surface area of a cube

How can we find the surface area of a cube of length x?

All six faces of a cube have the same area.

The area of each face is x × x = x2

Therefore,

x
Surface area of a cube = 6x2

Chequered cuboid problem

This cuboid is made from alternate purple and green centimetre cubes.

What is its surface area?

Surface area

=2×3×4+2×3×5+2×4×5

= 24 + 30 + 40

= 94 cm2

How much of the surface area
is green?

48 cm2

Surface area of a prism
What is the surface area of this L-shaped prism?

3 cm To find the surface area of this shape
3 cm we need to add together the area of
the two L-shapes and the area of the 6
rectangles that make up the surface of
4 cm the shape.

6 cm

Total surface area

= 2 × 22 + 18 + 9 + 12 + 6
+ 6 + 15

5 cm = 110 cm2

Using nets to find surface area

It can be helpful to use the net of a 3-D shape to calculate its surface area.

Here is the net of a 3 cm by 5 cm by 6 cm cuboid

6 cm Write down the area
of each face.
3 cm 18 cm2 3 cm
6 cm
Then add the areas
together to find the
5 cm 15 cm2 30 cm2 15 cm2 30 cm2 surface area.

3 cm 18 cm2 3 cm
Surface Area = 126 cm2

Making cuboids

The following cuboid is made out of interlocking cubes.

How many cubes does it contain?

Making cuboids

We can work this out by dividing the cuboid into layers.

The number of cubes in each layer can be
found by multiplying the number of cubes along
the length by the number of cubes along the
width.

3 × 4 = 12 cubes in each layer

There are three layers altogether so the total
number of cubes in the cuboid = 3 × 12 = 36
cubes

Making cuboids

The amount of space that a three-dimensional object takes up is called its
volume.

Volume is measured in cubic units.

For example, we can use mm3, cm3, m3 or km3.

The 3 tells us that there are three dimensions, length, width and height.

Liquid volume or capacity is measured in ml, l, pints or gallons.

Volume of a cuboid

We can find the volume of a cuboid by multiplying the area of the base by the
height.

The area of the base

= length × width

So,

height, h
Volume of a cuboid

= length × width × height

= lwh
length, l
width, w

Volume of a cuboid

What is the volume of this cuboid?

Volume of cuboid

= length × width × height
5 cm
= 5 × 8 × 13

8 cm 13 cm = 520 cm3

Volume and displacement

By dropping cubes and cuboids into a measuring cylinder half filled with water
we can see the connection between the volume of the shape and the volume of
the water displaced.

1 ml of water has a volume of 1 cm3

For example, if an object is dropped into a measuring cylinder and displaces 5
ml of water then the volume of the object is 5 cm3.

What is the volume of 1 litre of water?

1 litre of water has a volume of 1000 cm3.

Volume of a prism made from cuboids

What is the volume of this L-shaped prism?

3 cm
We can think of the shape as two
3 cm cuboids joined together.

4 cm Volume of the green cuboid

= 6 × 3 × 3 = 54 cm3
6 cm
Volume of the blue cuboid

= 3 × 2 × 2 = 12 cm3

Total volume
5 cm = 54 + 12 = 66 cm3

Volume of a prism

Remember, a prism is a 3-D shape with the same cross-section
throughout its length.

3 cm We can think of this prism as lots of L-
shaped surfaces running along the length of
the shape.

Volume of a prism

= area of cross-section × length

If the cross-section has an area of 22 cm2
and the length is 3 cm,

Volume of L-shaped prism = 22 × 3 = 66 cm3

Volume of a prism

What is the volume of this prism?

12 m

4m
7m
3m

5m

Area of cross-section = 7 × 12 – 4 × 3 = 84 – 12 = 72 m2
Volume of prism = 5 × 72 = 360 m3

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