The cuboid below is drawn on isometric paper. Every step from one dot to the next dot along an edge is 1 unit, and the three hidden edges are drawn with dashes. How many unit cubes would it take to build this cuboid?
Number of unit cubes = 4 × 2 × 3 = 24
Ans: 24
Example 1
Draw a cuboid 5 units by 2 units by 2 units on the isometric paper below. Every step from one dot to the next dot is 1 unit. Draw the hidden edges with dashes.
The 3 hidden edges are dashed
Ans: See figure: a cuboid 5 units by 2 units by 2 units drawn from one lowest vertex, with the three edges that meet at the back-bottom corner dashed and the other nine solid.
How to solve it
Find the lowest vertex. Three edges leave it: one going right and up, one going left and up, and one going straight up.
Count the steps between dots, not the dots. 5 dots in a row have only 4 steps, so the length is 4 units.
Do the same for the other two edges: 3 dots make a breadth of 2 units, and 4 dots make a height of 3 units.
Multiply the three counts: 4 times 2 times 3 is 24 unit cubes.
To draw a cuboid, count out the 3 edges from the lowest vertex, finish the solid, and dash the 3 edges at the back corner.
The lowest vertex is where the 3 edges of a drawing start. A step from one dot to the next is 1 unit. The 3 dashed edges are the corner at the back.
Practice questions with worked solutions
Questions 1 and 3 are free to try. The other 3 open in the free trial, each with its full working.
Count 4 steps for the length, 4 steps for the breadth and 4 steps up for the height. The far end of each of those 3 edges is a vertex next to the lowest one.
Complete the solid: 6 more edges, and each one is parallel to an edge already drawn.
Draw the 3 edges that meet at the back-bottom corner with dashes, because they are behind the solid.
Answer: See figure: a cube of edge 4 units drawn from one lowest vertex, with the three edges that meet at the back-bottom corner dashed and the other nine solid.
Question 3 of 5 · Intermediate · free to tryThe cuboid below is drawn on isometric paper. Every step from one dot to the…The cuboid below is drawn on…
The cuboid below is drawn on isometric paper. Every step from one dot to the next dot along an edge is 1 unit, and the three hidden edges are drawn with dashes. How many unit cubes would it take to build this cuboid?
How do you count cubes in P5 isometric drawing questions?
This page teaches drawing cubes and cuboids on an isometric grid and building solids with unit cubes, two outcomes in the Primary 5 Area and Volume strand.
What your child learns here
This page teaches drawing cubes and cuboids on an isometric grid and building solids with unit cubes, two outcomes in the Primary 5 Area and Volume strand. Your child reads lengths off the grid and finds the number of unit cubes.
One step between neighbouring dots is one unit.
Three edges leave the lowest vertex: one right and up, one left and up, and one straight up.
The number of unit cubes in a cuboid is length × breadth × height, counted in steps.
To draw a cuboid from a number of cubes and a base, find the height first by dividing the cubes by the number in one layer.
Edges that cannot be seen are drawn dashed, so the drawing shows which corner is at the back.
Does the answer make sense?
The number of unit cubes your child counts in a cuboid must be a whole multiple of the cubes in its bottom layer, one copy for each layer. When the upper layers are smaller than the base, the count must be less than a full cuboid of the same height.
How to practise these questions
Basic practice trains counting a cube's edge off the grid and working out how many unit cubes it holds. Intermediate questions add cuboids to count and drawings your child makes from given lengths or volumes. The Challenge question counts unit cubes layer by layer in a solid whose top layer is not complete. If the drawing or the count goes astray, watch the solution film for that question and come back to it later from Revision.
Questions parents ask
What is an isometric grid? It is a grid of dots arranged in triangles, used to draw solids so that three faces show. Each step between neighbouring dots stands for one unit.
Is isometric drawing in the Primary 5 syllabus? Yes. Drawing cubes and cuboids on isometric grid is an outcome under Volume of Cube and Cuboid in Primary 5.
Where can I get isometric paper? It can be printed free from many maths websites, or drawn by hand on dotted paper. A printed sheet keeps the dots evenly spaced.
