Measures and solids · Ages 12–13

Drawing solids on paper worksheet

Part of: 3-D figures

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Measures and solids · Ages 12–13

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Write each answer in the space. For word problems, show your working and write a sentence answer.

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, 17 cm wide and 20 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 16 cm long, 20 cm wide and 19 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:
4.An oblique drawing of a cube with 17 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.The solid is built of equal cubes, every column standing on the ground. How many cubes are there?
Answer:

6.Which is a correct drawing of a prism on a 3-sided base? (Edges out of sight are dashed.)
- A
- B
- C
- D
Choose the right picture
Answer:
7.Which is a correct drawing of a pyramid on a 6-sided base? (Edges out of sight are dashed.)
- A
- B
- C
- D
Choose the right picture
Answer:
8.An oblique drawing of a cuboid 13 cm long, 9 cm wide and 16 cm high, its front the length × height face. In the drawing the front is a rectangle 13 cm by 16 cm.
True or false?
Answer:
9.Which is a correct drawing of a pyramid on a 7-sided base? (Edges out of sight are dashed.)
- A
- B
- C
- D
Choose the right picture
Answer:
10.Drawing a cuboid 9 cm by 11 cm by 3 cm as seen from above and to one side, 3 of its edges are dashed.
True or false?
Answer:
11.Drawing an upright prism on a 7-sided base as seen from above and to one side, which face is always completely out of sight?
- A. Every face is in view
- B. The top face
- C. The side facing you
- D. The bottom face
Choose the right answer
Answer:
12.Drawing a cuboid 13 cm by 2 cm by 3 cm as seen from above and to one side, 6 of its edges are dashed.
True or false?
Answer:

13.In an oblique drawing of a cuboid, the front is a rectangle 8 cm by 9 cm and each edge going back is drawn 7 cm (half its real length). What is the cuboid's volume, in cm³?
Working:
Answer:
14.On grid paper, an oblique drawing of a cuboid 5 squares long, 2 wide and 11 high, its front the length × height face, edges going back drawn half length. What do its 12 edges (dashed ones too) add up to, in squares?
Working:
Answer:
15.The solid is built of cubes, every column on the ground. At least how many more cubes make it a 3 × 3 × 3 cube?
Working:
Answer:
16.An oblique drawing of a cuboid 10 cm by 6 cm by 6 cm, edges going back drawn half length; the 8 edges of the front and back faces make 64 cm. Find all the edges' total length: put the steps in order.
- A. All 4 going back = 4 × 3 = 12
- B. Total = 12 + 64 = 76
- C. One going back = 6 ÷ 2 = 3
Write the letters in the right order
Working:
Answer:
17.A supermarket stacks equal boxes as in the picture, every pile standing on the floor. How many boxes are there?
Working:
Answer:
18.The solid is built of cubes, every column on the ground. At least how many more cubes make it a cuboid 3 wide, 2 deep and 3 high?
Working:
Answer:

Show the answers and working

Drawing solids on paper worksheet: Answers and working

1. 15 cubes
Count each column's height, hidden cubes too: front 5 + 1 + 0, back 5 + 3 + 1, 15 in all.
2. 8.5 cm
The width, 17 cm, goes back, drawn half: 17 ÷ 2 = 8.5 cm. Length and height are on the front, drawn true.
3. 10 cm
The width, 20 cm, goes back, drawn half: 20 ÷ 2 = 10 cm. Length and height are on the front, drawn true.
4. 170 cm
The 8 edges of the front and back faces are drawn true: 8 × 17 = 136; the 4 going back at half: 4 × 8.5 = 34; 136 + 34 = 170 cm in all.
5. 27 cubes
Row by row: back 5 + 4 + 2, middle 4 + 2 + 2, front 4 + 2 + 2: 27 in all. The hidden columns stand on the ground too.

6. B
A prism has a top and a bottom; edges in view are solid, hidden ones dashed, and the outline is always in view.
7. A
A pyramid has one base and sides meeting at the apex; edges in view are solid, hidden ones dashed, none left out.
8. True
In an oblique drawing the front is drawn true, 13 cm by 16 cm; only the edges going back (the width, 9 cm) are halved.
9. D
A pyramid has one base and sides meeting at the apex; edges in view are solid, hidden ones dashed, none left out.
10. True
Just one corner of a cuboid is out of sight (at the back, underneath), and the 3 edges meeting there are dashed, whatever its size.
11. D. The bottom face
From above to one side you see the top and the sides facing you; the bottom is hidden behind the solid, and of its edges only those on the outline are solid, the rest dashed.
12. False
Just one corner of a cuboid is out of sight (at the back, underneath), and the 3 edges meeting there are dashed, whatever its size.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 1008 cm³
The front is its true size; the edges going back are halved, so really 2 × 7 = 14 cm. Volume: 8 × 9 × 14 = 1008.
14. 68 squares
The front and back faces' lengths and heights are true: 4 × 5 + 4 × 11; the 4 edges going back are 1 each: 4 × 1; 68 in all.
15. 14 cubes
The big cube takes 27 and there are 13 (hidden ones counted): 27 − 13 = 14.
16. C → A → B
Only the edges going back are halved: one, then all 4, then add the front and back faces' 64 cm.
17. 4 boxes
Pile by pile, hidden boxes too: front 1 + 0 + 0, back 1 + 1 + 1, 4 in all.
18. 7 cubes
The cuboid takes 3 × 2 × 3 = 18 cubes and there are 11: 18 − 11 = 7.

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