Introduction to 3D Shapes

Show your work for each problem.

1.
Which of these is a 3D shape?
1. a)Triangle
2. b)Square
3. c)Cube
4. d)Circle
Answer: Cube
A cube is a 3D shape with 6 square faces. Circles, squares, and triangles are all flat 2D shapes.
2.
How many faces does a cube have?
1. a)8
2. b)6
3. c)4
4. d)12
Answer: 6
A cube has 6 faces: top, bottom, front, back, left side, and right side. Each face is a square.
3.
A cube has 8 vertices. How many edges does it have?
Answer: 12
A cube has 12 edges. There are 4 edges around the top, 4 around the bottom, and 4 vertical edges connecting them.
4.
Which 3D shape has no edges and no vertices?
1. a)Cube
2. b)Pyramid
3. c)Cylinder
4. d)Sphere
Answer: Sphere
A sphere is perfectly round with 1 curved face, 0 edges, and 0 vertices. A ball is an example of a sphere.
5.
How many faces does a cylinder have? (Include curved surfaces)
Answer: 3
A cylinder has 3 faces: 2 flat circular faces (top and bottom) and 1 curved face that wraps around the side.
6.
A triangular prism has 2 triangular faces and 3 rectangular faces. How many faces, edges, and vertices does it have in total?
Answer: 5 faces, 9 edges, 6 vertices
1. How many faces does a triangular prism have? (triangular + rectangular) 5
2. How many edges does each triangular face have? 3
3. How many edges connect the two triangular faces? 3
4. Total edges: edges on both triangles plus connecting edges? 9
5. How many vertices does each triangular face have? 3
6. Total vertices (one set at each end of the prism)? 6
7.
Which 3D shape has 5 faces, 8 edges, and 5 vertices?
1. a)Square pyramid
2. b)Triangular prism
3. c)Cone
4. d)Cube
Answer: Square pyramid
A square pyramid has 1 square base + 4 triangular faces = 5 faces. It has 4 edges on the base + 4 edges going to the top = 8 edges. It has 4 corners on the base + 1 point at the top = 5 vertices.
8.
A cone has 1 circular base and comes to a point at the top. How many vertices does a cone have?
Answer: 1
A cone has only 1 vertex at the apex (the point at the top). The circular base has no vertices because a circle has no corners.
9.
A rectangular prism (like a box) has 6 faces. Count the edges and vertices.
Answer: 12 edges, 8 vertices
1. How many edges does the top rectangular face have? 4
2. How many edges does the bottom rectangular face have? 4
3. How many vertical edges connect the top and bottom? 4
4. Total number of edges? 12
5. How many vertices on the top face? 4
6. Total vertices (top + bottom)? 8
10.
A soda can is an example of which 3D shape?
1. a)Sphere
2. b)Rectangular prism
3. c)Cylinder
4. d)Cone
Answer: Cylinder
A soda can is a cylinder. It has 2 circular faces (top and bottom) and 1 curved surface wrapping around the sides.
11.
A hexagonal prism has two hexagonal faces (6-sided) connected by rectangular faces. Calculate the total number of faces, edges, and vertices.
Answer: 8 faces, 18 edges, 12 vertices
1. How many hexagonal faces are there? 2
2. How many rectangular faces connect the hexagons? 6
3. Total faces? 8
4. How many edges does one hexagon have? 6
5. How many edges connect the two hexagonal faces? 6
6. Total edges? 18
7. How many vertices does one hexagon have? 6
8. Total vertices? 12
12.
Using Euler's formula (), if a shape has 6 faces and 8 vertices, how many edges does it have?
1. a)10
2. b)14
3. c)16
4. d)12
Answer: 12
Using Euler's formula: , so , which gives , so . This matches a cube!
13.
A pentagonal pyramid has a 5-sided base and triangular faces meeting at an apex. How many edges does it have?
Answer: 10
A pentagonal pyramid has 10 edges: 5 edges around the pentagonal base + 5 edges going from each base vertex to the apex. It also has 6 faces (1 pentagon + 5 triangles) and 6 vertices (5 on base + 1 apex).
14.
Compare a cone and a cylinder. Which properties are the same and which are different?
Answer: Cylinder: 3 faces, 2 edges, 0 vertices. Cone: 2 faces, 1 edge, 1 vertex. Both have circular bases and curved surfaces.
1. How many flat circular faces does a cylinder have? 2
2. How many flat circular faces does a cone have? 1
3. How many curved faces does each shape have? 1
4. How many edges does a cylinder have? 2
5. How many edges does a cone have? 1
6. How many vertices does a cylinder have? 0
7. How many vertices does a cone have? 1
15.
An ice cream cone (the cone part only, not the ice cream) is what 3D shape? How many faces does it have?
Answer: 2
An ice cream cone is a cone shape. It has 2 faces: 1 circular face (the opening) and 1 curved face (the outside surface). It has 1 edge and 1 vertex (the point at the bottom).
16.
Which part of a 3D shape is where two faces meet?
1. a)Face
2. b)Edge
3. c)Vertex
4. d)Base
Answer: Edge
An edge is where two faces meet. It forms a line along the shape. For example, a cube has 12 edges where its 6 square faces connect.
17.
Match these real-world objects to their 3D shapes: a basketball, a dice, a tent (triangular), and a toilet paper roll.
Answer: Basketball = Sphere, Dice = Cube, Tent = Triangular prism, Toilet paper roll = Cylinder
1. What 3D shape is a basketball? (perfectly round) sphere
2. What 3D shape is a dice? (6 square faces) cube
3. What 3D shape is a triangular tent? triangular prism
4. What 3D shape is a toilet paper roll? cylinder