3-D figures · Ages 12–13
Nets of solids
Count the faces; in a cube's net, squares one apart in a line are opposite.
How to do it
Method
Count the faces; in a cube's net, squares one apart in a line are opposite
A pentagonal prism's net: 5 rectangles + 2 pentagons
Another way
Fold it in your head
Keep one face down and fold the others up one at a time
In full
Cut a solid along some edges and lay it flat: the flat shape is a net. Count the faces first. An n-sided prism's net has n rectangles and 2 n-sided bases, one on each side of the rectangles; an n-sided pyramid's, one n-sided base and n triangles; a cylinder's, a rectangle and two circles, the rectangle as long as the base's circumference; a cone's, a sector and a circle, the sector's arc as long as the base's circumference. A cube has 11 nets: 6 squares, never a 2 × 2 block, at most 4 in a line. To find opposite faces: two squares in a line with one between them end up opposite, and opposite faces never touch. Or fold it in your head: keep one face as the bottom and fold the others up one by one.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A net of a prism on a 9-sided base is made of rectangles and 9-sided polygons.
Fill in each blank
Show the answer and working
Answer: 9, 2
Its 9 sides are rectangles and its top and bottom are two 9-sided polygons.
Example 2
The net in the picture is folded into a cube. What do the numbers on the four faces next to 2 (sharing an edge with it) add up to?
Show the answer and working
Answer: 13
1 to 6 add up to 21. The faces next to 2 are all but itself and 6, opposite it: 21 − 2 − 6 = 13.
Example 3
Folded into a cube, the faces marked 6 and 2 are opposite each other.
True or false?
Show the answer and working
Answer: True
Opposite faces never touch, and squares one apart in a line are opposite. Folded, the face opposite 6 is 2.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A prism's net has 10 rectangles. How many polygons does the net have in all?
Answer:
2.A net of a prism on a 4-sided base is made of rectangles and 4-sided polygons.
Fill in each blank
Answer:
3.The six squares in the picture fold into a cube.
True or false?
Answer:
4.A cone's net is a sector and a circle. What is the sector's arc as long as?
- A. The base's diameter
- B. The cone's height
- C. The sector's radius
- D. The base's circumference
Choose the right answer
Answer:
5.Folded into a cube, the faces marked 5 and 1 are opposite each other.
True or false?
Answer:
All the answers
- 1. 12 polygons
- 2. 4, 2
- 3. True
- 4. D. The base's circumference
- 5. True
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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