The document provides information about topics for a geometry class including 3D shapes, surface area, volume, and nets. It defines 2D and 3D shapes, gives examples of dimensions of 3D objects, and discusses how to find the surface area and volume of common 3D shapes such as cubes and cuboids. It also explains what nets are and provides examples of common nets that can be used to form 3D shapes like cubes, prisms, pyramids, and cylinders.

1. Topics for today’s class:
3D shapes
Surface Area
Volume
Nets

2. Dimensions
2D shapes have 2 dimensions – e.g. length and width.
3D shapes have 3 dimensions – e.g. length, width and height.
e.g. The container below is 12 m long, 5 m wide and 3 m high.
The dimensions of this container are 12 m by 5 m by 3 m, which can also be written
as 12 m x 5 m x 3 m
3D Shapes
2D shapes are flat objects. 3D shapes are solid objects. The surfaces of 3D shapes are
called faces.

4. Working with Dimensions

5. Example: Working with Dimensions
Leonardo is designing a box to hold 5 DVD cases.
Each DVD case is 14 cm long, 1.4 cm wide and 19 cm high.
Sketch a box that could hold the DVD cases. Give the dimensions.
Each DVD is 1.4 cm wide. It would make sense to put them side by side in a row, such as:
Each DVD case is 1.4 cm wide, therefore 5 DVD cases will be:
1.4 × 5 = 7 cm wide
Therefore, the box needs to be at least 7 cm wide.
The DVD cases are 14 cm long and 19 cm high, so the box needs to be at least 14 cm
long and 19 cm high.
Therefore, you could sketch a box
(making sure to label the dimensions), such as:

6. QUESTION:
Jamie is packing 6 identical books into a box. He lays them down and stacks them. Each book is 25 cm
long, 35 cm high and 8 cm wide.
What is the minimum height the box needs to be?
If the books are stacked on top of each other laid down, with 8 cm now being the height of the book laid
down, then the minimum height of the box must be
6×8=48 cm

7. Nets
A net is a 3D shape that has been unfolded. You need to be able to recognize and draw
nets.

8. Understanding Nets
A net shows each face of a shape laid out flat. 3D shapes often have several different nets. Below
are some examples of nets of a cube
Each net can
be folded up
to construct a
cube

9. Nets of Other Shapes
There are some other common nets of 3D shapes that you should be familiar with.
A prism is a shape with two identical 2D shapes that are joined by rectangular faces. The net of a prism will feature
the 2D shape at both ends with rectangles between them. A cuboid is also a type of prism, so the net of a cuboid
follows the same pattern.
A pyramid will feature a 2D shape as its base, e.g. a triangle or a square, with each edge linked to a triangular
face. These triangular faces all meet at a central point above the centre of the base. The net of a pyramid consists
of the base, with triangles connected to each edge of the base.
A cylinder is similar to a prism, in that it has two identical faces at each end. The curved section that connects the
two circles forms a rectangle when it is stretched out.

11. Question 1: Which of the following nets can be used to form a cube?
A and C will form a cube.
The faces on B will overlap when folded over and D has
too many faces.
So, A and C are the only nets that can form a cube.
Question 2: Sketch a net of the following cuboid,
labelling your measurements.
The completed sketch should look like this:

12. Surface Area

15. Practice Question
Below is a cuboid with length 6 mm, width 2.5 mm, and height 4 mm.
Calculate the surface area of the cuboid.

16. Practice Question

18. Volume

20. QUESTION:
The diagram below shows the outline of a cuboid, ABCDEFGH, with dimensions:
AB=3 cm, BC=12 cm, and CF=16 cm.
Calculate the volume of the cuboid.
Multiply the length by the height by the width:
Volume = 3 × 12 × 16 = 576 cm^3