Measures and solids · Ages 12–13

Nets of solids worksheet

Part of: 3-D figures

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Measures and solids · Ages 12–13

Numsprite
numsprite.com

Name:Date:Score:／48

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

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 5-sided base is made of rectangles and 5-sided polygons.
Fill in each blank
Answer:
3.A net of a prism on a 7-sided base is made of rectangles and 7-sided polygons.
Fill in each blank
Answer:
4.The net in the picture is folded into a cube. What number is on the face opposite 1?
Answer:
5.Take π as 3.14. A cylinder has base radius 10 cm and height 3 cm. In its net, how long is the rectangle (the base's circumference), in cm?
Answer:
6.The net in the picture is folded into a cube. What do the numbers on the four faces next to 3 (sharing an edge with it) add up to?
Answer:
7.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?
Answer:

8.Which of these is a net of the solid in the picture?
- A
- B
- C
- D
Choose the right picture
Answer:
9.Which of these is a net of a pyramid on a 8-sided base?
- A
- B
- C
- D
Choose the right picture
Answer:
10.The six squares in the picture fold into a cube.
True or false?
Answer:
11.A cone's net is a sector and a circle. What is the sector's arc as long as?
- A. The cone's height
- B. The base's circumference
- C. The base's diameter
- D. The sector's radius
Choose the right answer
Answer:
12.Folded into a cube, the faces marked 3 and 2 are opposite each other.
True or false?
Answer:

13.Take π as 3.14. A can is a cylinder of radius 10 cm and height 7 cm, its label covering the whole curved side. What is the label's area, in cm²?
Working:
Answer:
14.A net of a cube is drawn from 6 squares of side 7 cm, joined edge to edge. Whichever net it is, what is its perimeter, in cm?
Working:
Answer:
15.A funnel is a cone with base radius 4 cm and slant 10 cm. What is the angle of the sector in its net, in degrees?
Working:
Answer:
16.A gift box is a prism on a 7-sided base of area 23 cm², each side 2 cm, 5 cm high. In its net the rectangles make cm², the two bases cm², cm² in all.
Fill in each blank
Working:
Answer:
17.Take π as 3.14. A paper party hat is a cone with base radius 6 cm. How long is the arc of the sector it is made from, in cm?
Working:
Answer:
18.A closed box 12 cm long, 9 cm wide and 10 cm high is made of card (no flaps). In its net the length × width faces are cm², the length × height faces cm², the width × height faces cm², two of each, cm² in all.
Fill in each blank
Working:
Answer:

Show the answers and working

Nets of solids worksheet: Answers and working

1. 12 polygons
The 10 rectangles are its sides; add its 2 bases: 10 + 2 = 12.
2. 5, 2
Its 5 sides are rectangles and its top and bottom are two 5-sided polygons.
3. 7, 2
Its 7 sides are rectangles and its top and bottom are two 7-sided polygons.
4. 4
Opposite faces never touch once folded: squares one apart in a line end up opposite, or fold it in your head. Opposite 1 is 4.
5. 62.8 cm
Rolled up, the rectangle is the curved surface, its length going once round the base: 2 × 3.14 × 10 = 62.8. The height, 3 cm, is its width.
6. 17
1 to 6 add up to 21. The faces next to 3 are all but itself and 1, opposite it: 21 − 3 − 1 = 17.
7. 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.

8. D
Know the solid first: a prism's net has 2 bases and a row of rectangles, a base on each side of the row; a pyramid's has one base with a triangle on each side. Then count the base's sides: 7.
9. B
A net of a pyramid on a 8-sided base: the 8-sided base with a triangle on every side, 8 triangles meeting at the apex when folded.
10. False
A cube's net never has a 2 × 2 block or more than 4 squares in a line; folded, the six squares take a face each, none overlapping.
11. B. The base's circumference
Folded up, the sector's arc runs once round the base's edge, so it is as long as the base's circumference.
12. False
Opposite faces never touch, and squares one apart in a line are opposite. Folded, the face opposite 3 is 6.

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

13. 439.6 cm²
Unrolled, the label is a rectangle as long as the circumference, 2 × 3.14 × 10 = 62.8, and 7 wide: 62.8 × 7 = 439.6.
14. 98 cm
6 squares have 24 sides; joining them into one net takes 5 joins, each hiding 2 sides: 24 − 10 = 14 sides, 14 × 7 = 98.
15. 144°
The sector's radius is the slant, 10 cm, and its arc the base's circumference, 2π × 4: 410 of the full circle 2π × 10, so the angle is 360° × 4 ÷ 10 = 144°.
16. 70, 46, 116
7 rectangles of 2 × 5: 7 × 2 × 5 = 70; two bases, 2 × 23 = 46; 116 in all.
17. 37.68 cm
The arc goes once round the rim, the base's circumference: 2 × 3.14 × 6 = 37.68.
18. 108, 120, 90, 636
A cuboid's six faces are three matching pairs: 2 × (108 + 120 + 90) = 636.

Numsprite · numsprite.com/en/worksheets/3d-figures/nets-of-solids