Properties of 3-D shapes worksheet

Part A: Working out and filling in

1. 1. A pentagonal pyramid has 10 edges

   The base has 5 edges, and one runs from the top to each corner of it: 5 × 2 = 10, so 10 edges

2. 2. This prism has 16 vertices

   Its base is an octagon, with 8 sides. The top and the bottom have 8 vertices each: 8 × 2 = 16, so 16 vertices

3. 3. This pyramid has 9 vertices

   Its base is an octagon, with 8 sides. The base has 8 vertices, and the top is one more: 8 + 1 = 9, so 9 vertices

4. 4. A hexagonal pyramid has 7 faces

   A pyramid has 1 base and a triangle on each of the base's sides: 6 + 1 = 7, so 7 faces

5. 5. This prism has 5 faces

   Its base is a triangle, with 3 sides. A prism has 2 bases and 3 faces round the side: 3 + 2 = 5, so 5 faces

6. 6. A cuboid has 8 vertices

   The top and the bottom have 4 vertices each: 4 × 2 = 8, so 8 vertices

7. 7. This pyramid has 4 vertices

   Its base is a triangle, with 3 sides. The base has 3 vertices, and the top is one more: 3 + 1 = 4, so 4 vertices

8. 8. This prism has 15 edges

   Its base is a pentagon, with 5 sides. The top and the bottom have 5 edges each, and 5 more run up the side: 5 × 3 = 15, so 15 edges

9. 9. A hexagonal pyramid has 7 vertices

   The base has 6 vertices, and the top is one more: 6 + 1 = 7, so 7 vertices

10. 10. A cube has 12 edges

    The top and the bottom have 4 edges each, and 4 more run up the side: 4 × 3 = 12, so 12 edges

11. 11. A hexagonal pyramid has 12 edges

    The base has 6 edges, and one runs from the top to each corner of it: 6 × 2 = 12, so 12 edges

12. 12. This pyramid has 6 faces

    Its base is a pentagon, with 5 sides. A pyramid has 1 base and a triangle on each of the base's sides: 5 + 1 = 6, so 6 faces

Part B: Word problems

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

1. 13. Tsz-ching makes a prism frame from straws. The prism's base has 6 sides, and each edge is one straw. How many straws does she need? (Answer: 18 straws)

   6 edges round the top, 6 round the bottom, 6 up the sides: 6 × 3 = 18

2. 14. May makes 3 cube frames from straws and clay. Each edge is one straw, and each corner is one ball of clay. How many straws does she need altogether? (Answer: 36 straws)

   A cube has 12 edges: 12 × 3 = 36

3. 15. Ka-yee makes a pyramid frame from clay balls and straws. The pyramid's base has 5 sides, and each corner is one ball of clay. How many balls of clay does she need? (Answer: 6 balls)

   5 corners round the base, and 1 at the top: 5 + 1 = 6

4. 16. Ka-yee makes a prism frame from straws. The prism's base has 4 sides, and each edge is one straw. How many straws does she need? (Answer: 12 straws)

   4 edges round the top, 4 round the bottom, 4 up the sides: 4 × 3 = 12

5. 17. Ka-yan makes a pyramid frame from clay balls and straws. The pyramid's base has 5 sides, and each corner is one ball of clay. How many balls of clay does she need? (Answer: 6 balls)

   5 corners round the base, and 1 at the top: 5 + 1 = 6

6. 18. A prism has a base with 8 sides. How many faces does the prism have altogether? (Answer: 10 faces)

   8 side faces, plus the top and the bottom: 8 + 2 = 10