Measures and solids · Ages 12–13

Prisms, pyramids and round solids 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.How many edges does a prism on a 8-sided base have?
Answer:
2.How many edges does a prism on a 10-sided base have?
Answer:
3.A prism on a 6-sided base has faces, edges and vertices.
Fill in each blank
Answer:
4.A pyramid on a 6-sided base has faces, edges and vertices.
Fill in each blank
Answer:
5.A prism has 24 edges. How many sides does its base have?
Answer:
6.A pyramid's edges and vertices number 10 in all. How many faces does it have?
Answer:
7.A pyramid's edges and vertices number 28 in all. How many faces does it have?
Answer:

8.The picture shows a right prism on a regular polygon. What is it called?
- A. A prism on a 10-sided base
- B. A pyramid on a 8-sided base
- C. A prism on a 9-sided base
- D. A prism on a 8-sided base
Choose the right answer
Answer:
9.The picture shows a pyramid on a regular polygon. What is it called?
- A. A prism on a 4-sided base
- B. A pyramid on a 4-sided base
- C. A pyramid on a 5-sided base
- D. A cone
Choose the right answer
Answer:
10.Which solid has 4 faces, 6 edges and 4 vertices?
- A
- B
- C
- D
Choose the right picture
Answer:
11.Besides one curved surface, the solid in the picture has this many flat faces: 1.
True or false?
Answer:
12.The picture shows a regular polyhedron. What shape is each of its faces?
- A. A square
- B. An equilateral triangle
- C. A regular hexagon
- D. A regular pentagon
Choose the right answer
Answer:

13.A pyramid has 26 edges. Find how many vertices it has: put the steps in order.
- A. Vertices = 13 + 1 = 14
- B. n = 26 ÷ 2 = 13
- C. 2n = 26
Write the letters in the right order
Working:
Answer:
14.A crystal is two pyramids on 10-sided bases stuck base to base. It has faces, edges and vertices.
Fill in each blank
Working:
Answer:
15.A frame of a prism on a 4-sided base uses 140 cm of wire, each side of its bases 8 cm. How long is each upright edge, in cm?
Working:
Answer:
16.A frame of a prism on a 10-sided base is made of straws and clay: one 27 cm straw for each edge, one ball of clay at each vertex. That takes straws and balls of clay, cm of straw in all.
Fill in each blank
Working:
Answer:
17.A wire frame of a pyramid on a 6-sided base: each side of the base is 17 cm and each slanting edge 15 cm. How many cm of wire does it take?
Working:
Answer:
18.A workshop makes 14 frames of prisms on 4-sided bases, with a joint at every vertex. How many joints does it need?
Working:
Answer:

Show the answers and working

Prisms, pyramids and round solids worksheet: Answers and working

1. 24 edges
8 round the top, 8 round the bottom and 8 upright: 8 × 3 = 24.
2. 30 edges
10 round the top, 10 round the bottom and 10 upright: 10 × 3 = 30.
3. 8, 18, 12
Faces: 6 sides and 2 bases, 8; edges: 6 top, 6 bottom, 6 upright, 18; vertices: 6 top and 6 bottom, 12.
4. 7, 12, 7
Faces: the base and 6 triangles, 7; edges: 6 round the base and 6 slanting, 12; vertices: 6 round the base and 1 at the top, 7.
5. 8 sides
A prism has 3 times as many edges as its base has sides (top, bottom and upright): 24 ÷ 3 = 8.
6. 4 faces
An n-sided pyramid has 2n edges and n + 1 vertices, 3n + 1 = 10 in all, so n = 3 and it has n + 1 = 4 faces.
7. 10 faces
An n-sided pyramid has 2n edges and n + 1 vertices, 3n + 1 = 28 in all, so n = 9 and it has n + 1 = 10 faces.

8. D. A prism on a 8-sided base
Two parallel bases, rectangular sides, and 8 sides to the base: a prism on a 8-sided base.
9. B. A pyramid on a 4-sided base
One base and triangular sides meeting at the apex, the base with 4 sides: a pyramid on a 4-sided base.
10. C
Tell prism from pyramid, then count the base's sides n: a prism has n + 2 faces, 3n edges, 2n vertices; a pyramid n + 1 faces, 2n edges, n + 1 vertices.
11. False
A cylinder has 2 circular bases, a cone 1, and a sphere no flat face at all, only its curved surface.
12. B. An equilateral triangle
A regular polyhedron's faces are of three kinds only: equilateral triangles (tetrahedron, octahedron, icosahedron), squares (cube) and regular pentagons (dodecahedron).

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

13. C → B → A
An n-sided pyramid has 2n edges, so n = 13; its vertices are the base's 13 and 1 at the top: 14.
14. 20, 30, 12
The glued bases are no longer faces: 10 + 10 = 20 faces; edges: the 10 shared base edges and 10 slanting ones above and below, 30; vertices: the base's 10 and the two tips, 12.
15. 19 cm
The two bases have 2 × 4 = 8 sides, 64 cm; the other 140 − 64 = 76 cm goes to 4 upright edges: 76 ÷ 4 = 19.
16. 30, 20, 810
The prism has 3 × 10 = 30 edges and 2 × 10 = 20 vertices; the straws make 30 × 27 = 810 cm.
17. 192 cm
The pyramid has 6 base edges and 6 slanting ones: 6 × 17 + 6 × 15 = 192 cm.
18. 112 joints
Each prism has 2 × 4 = 8 vertices: 8 × 14 = 112.

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