3-D figures · Ages 12–13
Drawing solids on paper
Hidden edges dashed; slanting edges half length.
How to do it
Method
Hidden edges dashed; slanting edges half length
A cuboid: one hidden corner, 3 dashed edges
Another way
Isometric drawing
Upright edges stay upright, lengths true
In full
There are two common ways to draw a solid on paper. An oblique drawing: draw the front face its true shape, then from each corner draw parallel slanting lines going back (usually half their real length), and join their ends for the back. An isometric drawing: on isometric dot paper, upright edges stay upright, the others slope to the left and right, every length true. Either way, edges you can't see are dashed and those you can see are solid; a cube or cuboid has just one corner out of sight, so the 3 edges at it are dashed. To count the cubes in a drawing of a stack, remember the ones hidden underneath: every column stands on the ground, so count each column's height and add them up.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
An oblique drawing of a cube with 7 cm edges: the front drawn its true size, the 4 edges going back half their real length. What is the total length of the 12 edges in the drawing (solid and dashed), in cm?
Show the answer and working
Answer: 70 cm
The 8 edges of the front and back faces are drawn true: 8 × 7 = 56; the 4 going back at half: 4 × 3.5 = 14; 56 + 14 = 70 cm in all.
Example 2
An oblique drawing of a cuboid 13 cm long, 3 cm wide and 10 cm high, its front the length × height face. In the drawing the front is a rectangle 13 cm by 10 cm.
True or false?
Show the answer and working
Answer: True
In an oblique drawing the front is drawn true, 13 cm by 10 cm; only the edges going back (the width, 3 cm) are halved.
Example 3
The solid is built of equal cubes, every column standing on the ground. How many cubes are there?
Show the answer and working
Answer: 14 cubes
Row by row: back 3 + 2 + 2, middle 2 + 1 + 1, front 2 + 1 + 0: 14 in all. The hidden columns stand on the ground too.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The solid is built of equal cubes, every column standing on the ground. How many cubes are there?
Answer:
2.An oblique drawing of a cuboid 19 cm long, 12 cm wide and 3 cm high: the front (length × height) drawn its true size, the edges going back half their real length. How long is each edge going back in the drawing?
Answer:
3.An oblique drawing of a cuboid 12 cm long, 18 cm wide and 13 cm high, its front the length × height face. In the drawing the front is a rectangle 12 cm by 13 cm.
True or false?
Answer:
4.An oblique drawing of a cube with 5 cm edges: the front drawn its true size, the 4 edges going back half their real length. What is the total length of the 12 edges in the drawing (solid and dashed), in cm?
Answer:
5.Drawing a cuboid 3 cm by 17 cm by 13 cm as seen from above and to one side, 3 of its edges are dashed.
True or false?
Answer:
All the answers
- 1. 14 cubes
- 2. 6 cm
- 3. True
- 4. 50 cm
- 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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