3-D figures · Ages 12–13
Three views
Front: each column's tallest; top: where there are cubes.
How to do it
Method
Front: each column's tallest; top: where there are cubes
A cone: a triangle from the front, a circle with its centre dot from above
Another way
Back from the views
Each place at most the smaller of its column's and row's tallest
In full
Looking at a solid from the front, the side (the right) and above gives three flat drawings: its three views. The front view shows height and width, the side view height and depth, the top view width and depth. For a stack of cubes, the front view draws each column across as tall as its tallest stack; the right view has the front row on its left and the back row on its right, each as tall as its tallest; the top view draws a square wherever there are cubes, whatever the height. Working back from the views: the top view says which places hold cubes, the front and side views how tall each column and row is at most. Each place can be at most the smaller of its column's and its row's tallest, and adding those gives the most cubes there can be.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Looking at the solid in the picture from the front, what shape do you see?
- A. A circle
- B. A triangle
- C. A square
- D. A rectangle
Choose the right answer
Show the answer and working
Answer: D. A rectangle
Stand right in front: a cube is a square, a cuboid or cylinder a rectangle, a cone, a pyramid or a triangular prism with its triangle to you a triangle, a sphere a circle.
Example 2
The solid is built of cubes, every column standing on the ground. How many squares do you see from the front?
Show the answer and working
Answer: 8 squares
Each column across shows only its tallest stack: 4 + 3 + 1 = 8; the shorter ones in front add nothing.
Example 3
The picture shows the three views of a solid built of cubes: the front view at the top left, the view from the right beside it (the front on its left), the view from above underneath (the back at the top). At most, how many cubes can it have?
Show the answer and working
Answer: 13 cubes
The view from above shows where the cubes stand; each place can be at most the smaller of its column's tallest (front view) and its row's tallest (right view). Added up, at most 13.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.Looking at the solid in the picture from the front, what shape do you see?
- A. A square
- B. A triangle
- C. A rectangle
- D. A circle
Choose the right answer
Answer:
2.The solid is built of cubes, every column standing on the ground. Which shape do you see from above?
- A
- B
- C
- D
Choose the right picture
Answer:
3.The solid is built of cubes, every column standing on the ground. How many squares do you see from above?
Answer:
4.The solid is built of cubes, every column standing on the ground. How many squares do you see from the front?
Answer:
5.Looking at the solid in the picture from above, which shape do you see?
- A
- B
- C
- D
Choose the right picture
Answer:
All the answers
- 1. B. A triangle
- 2. A
- 3. 7 squares
- 4. 9 squares
- 5. C
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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