Three-dimensional figures are a key part of the primary school Mathematics curriculum. One of the most basic three-dimensional figures is a cube! For some Mathematics questions, you will need to have a full understanding of what a cube is, so that you can apply your knowledge to solve a problem. After all, questions featuring cubes commonly pop up in the PSLE paper.

 

What exactly is a cube?

A cube is what happens when you make a square three-dimensional. If you’ve ever played with a standard pair of dice, you’ll know exactly what a cube is. What other items do you see around you in real life that are cubic?

 

All of the edges of a cube are of equal lengths

The first rule of a cube is that all its edges are of equal length – just like its base form, the square. We also know that a cube has 12 edges. Remember: an edge is a line segment where two surfaces meet!

All of the lines shown in the picture of the cube below, including the dotted lines, are edges.

 

A cube always has six equal faces

Another fact that primary school students in Singapore should know about cubes is that they all have six equal square faces. Faces refer to the flat areas on an object.

Each of the coloured squares on the cube below is a face.

 

CHECK POINT 1:

Imagine that a large cube is made up of 27 small cubes. John paints the entire outside of the large cube blue, then breaks the large cube back into 27 small cubes.

How many of the small cubes would have three painted faces?

 

Cubes have both surface area and volume

The surface area of a cube refers to the area covered by the outside of a cube, and can be calculated with a simple formula. 

Since all cubes have six equal square faces, the surface area of a cube can be calculated by multiplying 6 with the product of two edges.

In other words:

Surface area of a cube = 6 x edge x edge

or

Surface area of a cube = 6a2 (where a = the length of one edge)

 

The volume of a cube tells us how much space is enclosed by the boundaries of that cube. Finding the volume of an object can help us to determine the amount required to fill that object, like the amount of water needed to fill a bottle, an aquarium or a water tank. We can calculate the volume of a cube with a simple formula – by cubing the length of one edge!

In other words:

Volume of a cube = edge x edge x edge

or

Volume of a cube = a3 (where a = the length of one edge)

Don’t forget that volume must be presented in cubic units (e.g. cm3).

 

CHECK POINT 2:

The figure below is made up of small cubes. Each small cube has a side of 3cm. What is the total volume of the figure?

 

 

Cubes can be unfolded to create nets

A geometry net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid. 

Have you ever tried to make a die out of paper? In order to do so, you would have to cut out a continuous shape made out of (you know how many!) six squares connected together. This is also known as a net.

A cube has one top, one bottom (the two base faces) and four sides.

Did you know that there are 11 different ‘nets’ that can be made by unfolding a cube?

 

Can you solve this PSLE 2019 Mathematics question involving cubes?

Jack has 8 identical large cubes and some identical small cubes. He packs all the cubes tightly into a rectangular box such that cubes of the same size are stacked on top of each other. The box is filled to its brim exactly.

The figure below shows the first layer of cubes packed into the box.

  1. How many small cubes does Jack have? [1 mark]
  2. The volume of the box is 4032cm3. The total volume of the 8 large cubes is 37of the volume of the box. What is the length of one edge of the small cube? [3 marks]

 

Do you think you can use the facts you’ve learnt here to solve this PSLE Mathematics question? If you get stuck, you can watch our Head of Mathematics, TCHER Dicky, go through the solution on YouTube!

 

Pick up all these tips and more in our Mathematics online tuition classes at TCHER Online! Prepare your child for the PSLE safe and sound from the comfort of your own home, without wasting time on transport. 

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Book a free trial with us at TCHER Online – we offer English, Chinese, Maths and Science for many levels ranging from Primary to Secondary, with lessons purpose-written for online learning by ex-MOE teachers. 

 

 

ANSWERS:

Check Point 1: 8 

Check Point 2: 324cm3