Building a solid out of unit cubes is in the Primary 5 Volume chapter. The lesson film is the one Mathweave teaches this skill with in Primary 6, and the practice set below is chosen for Primary 5.
Lesson video, with the working
Front, Side and Top Views of a Solid
2 min 41 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
Solid P is built from unit cubes. The arrows show where you look from. (a) Draw the front view of Solid P. (b) Draw the side view of Solid P. (c) Draw the top view of Solid P. (d) How many unit cubes are used to build Solid P?
Total cubes = 4 (base) + 2 (middle) + 1 (top) = 7
Ans: 7
Example 1
Solid Q is built from 5 unit cubes. Draw the top view of Solid Q on the grid.
The top view is a 2 by 2 square of 4 unit squares.
Ans: 2 by 2 square
How to solve it
A view is the solid drawn flat from one side. Draw only what you see from the arrow's direction.
In the front view, a cube behind another lines up with it, so two cubes can show as one square.
For the side view, look in from the right. The front of the solid is on the left of the grid.
For the top view, you see the floor, 2 squares by 2 squares. It does not show how tall anything is.
To count the cubes, use the top view for the base layer, 4 cubes, then add the layers above: 7 unit cubes.
The top view has 4 squares. The solid has 5 cubes. A view is a shape, and the number of cubes is not in it.
Practice questions with worked solutions
Question 1 is free to try. The other 11 open in the free trial, each with its full working.
Question 1 of 12 · Basic · free to tryA solid is built from unit cubes. Its bottom layer is a rectangle 3 cubes…A solid is built from unit…
A solid is built from unit cubes. Its bottom layer is a rectangle 3 cubes long and 2 cubes deep. A second layer of 4 cubes sits on the left-hand 2 by 2 of it, and a third layer of 2 cubes sits on the left-hand column of that. How many unit cubes are used to build the solid?
How do you count the cubes in P5 unit cubes questions?
This page teaches building solids with unit cubes, the first outcome under Volume of Cube and Cuboid in Primary 5.
What your child learns here
This page teaches building solids with unit cubes, the first outcome under Volume of Cube and Cuboid in Primary 5. Your child counts a solid one layer at a time and uses its flat views to picture the cubes that cannot be seen.
Each unit cube is 1 cubic unit, so the number of cubes in a solid is its volume.
Count from the bottom layer up, since a cube on a higher layer always rests on one beneath it.
A front, side or top view is a flat shape with one square for each column seen from that side.
A full box of cubes holds length × breadth × height cubes, so the cubes still needed are the full box minus the cubes used.
When a painted block is taken apart, corner cubes have 3 painted faces, other edge cubes 2, face cubes 1 and inside cubes none.
Does the answer make sense?
In Question 1 every layer sits on the one below, so your child's total must be more than the 6 cubes of the bottom layer. A full block 3 long, 2 deep and 3 high would hold 18, and the upper layers are not full, so 12 sits sensibly between 6 and 18.
How to practise these questions
Question 1 is free: a solid has a bottom layer 3 cubes long and 2 cubes deep, with layers of 4 cubes and then 2 cubes above it, and your child counts every cube. Basic questions train counting layer by layer and drawing a top view on a grid. Intermediate questions use a front view and a depth, read a top view, and find the cubes that turn a part-built solid into a full cuboid. Challenge questions leave a corner out of a box, sort the cubes of a painted block by painted faces, and add hidden cubes without changing two views. If a count does not add up, open its worked solution and try again later from Revision.
Questions parents ask
How can my child count the cubes that are hidden? Count one layer at a time, starting from the bottom. Every cube on an upper layer needs a cube under it, so those hidden cubes still belong in the total.
Is building with unit cubes in the Primary 5 syllabus? Yes. Building solids with unit cubes and measuring volume in cubic units are the first two outcomes under Volume of Cube and Cuboid in Primary 5.
Can the top view tell you how many cubes a solid has? No. It shows which squares of the floor are covered, not how tall each column is. The layers, or the front and side views, give each column's height.
