FS Maths Level 2 - May 27, 2023 (Nets, 3D shapes (surface area and volume-2).

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