We solve problems by combining our knowledge of the classification of solids, nets, and orthographic views.
📘 Example ①
What shapes of paper are needed to cut out and make a net of a regular square pyramid?
Answer: 1 square (base) + 4 isosceles triangles (lateral faces)
What shapes of paper are needed to cut out and make a net of a regular square pyramid?
Answer: 1 square (base) + 4 isosceles triangles (lateral faces)
📘 Example ②
If the front, side, and top views of a solid are all circles, name the solid.
Answer: A sphere (it appears as a circle from every direction)
If the front, side, and top views of a solid are all circles, name the solid.
Answer: A sphere (it appears as a circle from every direction)
💡 Key Points
- Identify a solid from its net: focus on the shapes of the base and lateral faces
- Identify a solid from its orthographic views: combine the shapes from the three directions
Practice Problems
- What solid has rectangular front and side views and a circular top view?
- State the numbers of faces, edges, and vertices of a triangular prism.
Answers and Explanations
- Answer: A cylinder.
- Answer: 5 faces (2 triangles+3 rectangles), 9 edges, and 6 vertices.