Mathweave
Menu
Lessons How it works Pricing AboutSign inStart your free trialFree trial

Primary 6 · Solids · Question type 10.2

P6 Solids: Adding and Removing Cubes from Views

At each position, the greatest column height is the smaller of its front-view and side-view heights.

Try the question yourself, or watch the lesson first.

Primary 6, on the MOE Primary Mathematics syllabus.

In the Solids chapter4 question types · see the chapter

The lesson · 2 minutes 48 seconds

How do front and side views show cubes added or removed in P6?

Watch: 9 unit cubes on a table, and the greatest number that can be added without changing what the front and the side show

Another worked example

A worked example

Solid C is built from 16 unit cubes on a table: a full layer of 9, a tower 4 cubes high at the front left corner, a tower 4 cubes high at the back right corner, and one extra cube on the middle column. More cubes are added, each resting on the table or on another cube. What is the greatest number of cubes that can be added without changing the front view or the side view?

The working · Eight lines

The step-by-step working

Written out in full, the way it should appear on paper.

  1. front view heights, left to right, are 4, 2 and 4
  2. side view heights, front to back, are 4, 2 and 4
  3. each column can stand as tall as the smaller of its two view heights
  4. front row of the footprint, left to right = 4 + 2 + 4 = 10
  5. middle row of the footprint = 2 + 2 + 2 = 6
  6. back row of the footprint = 4 + 2 + 4 = 10
  7. tallest solid with these two views = 10 + 6 + 10 = 26
  8. cubes that can be added = 26 - 16 = 10

The answer is 10.

Practise · Modelled on top school exam questions

Try a different question

Try it yourself first. Open the solution when you want to see the steps. No sign-up is needed. These questions are written by Mathweave, not copied from school papers.

Try it yourself

Count the cubes hidden from the front

Compare the visible squares with the total number of cubes.

Solid A is built from 9 unit cubes. Looking at it from the front, three columns of squares are seen, 3 squares high, 2 squares high and 2 squares high. How many of the 9 cubes does the front view not show?

Show the step-by-step solution
  1. front view squares = 3 + 2 + 2 = 7
  2. cubes in the solid = 9
  3. cubes the front view does not show = 9 - 7 = 2

Ans: 2

Keep practising

The practice plan adds more questions and saved progress.

See practice plans See how practice works

Choose your next step

Next, count the painted faces on glued cubes. Drawing Shapes on a Grid →

← Back to the chapter: three questions and all the lessons