CBSE Notes Class 7 Maths Chapter 13 Visualising Solid Shapes

Chapter 13, "Visualizing Solid Shapes," introduces 3D solids and their 2D representations. It explores how solids like cubes, spheres, and cones can be visualized through top, front, and side views. The chapter also explains nets, which are flat layouts of solids, helping students understand the structure, properties, and geometry of three-dimensional shapes effectively.

1.0Geometric Solids

1. Geometric solids are 3D figures with length, width, and height.
2. Edges, vertices, and faces: Every solid has a fixed number of these elements.
3. Faces: Flat or curved 2D surfaces.
4. Surface types: Solids can have flat surfaces, curved surfaces, or both.
5. Polyhedron: A solid with only flat surfaces; each surface is called a face.
6. Edges: Formed where two faces meet.
7. Vertices: Points where three or more edges converge.
8. 2D shapes: Have only length and width, unlike 3D solids.

2.0Geometric Properties

1. Prism

• Definition: A prism is a solid with two parallel, congruent polygonal bases.
• Lateral faces: The other faces are parallelograms and are called lateral faces.
• Height: The perpendicular distance between the bases is the height of the prism.
• Right prism: A prism where the bases are perpendicular to the lateral faces.
• Cross-section: A section parallel to the base, identical in shape and size to the base.
• Naming: Prisms are named based on the shape of their bases.
• Top and base: Both are identical in shape and size.

2. Cuboid

• A cuboid is a solid with six rectangular faces. Opposite faces have the same shapes and sizes.
• If length, breadth and height of cuboid become equal, then it will be a cube.

3. Cube 

A cube is a special type of cuboid with six square faces of the same size. All the edges are equal in length.

4. Pyramid

• Definition: A pyramid is a solid with a polygonal base and triangular lateral faces.
• Common vertex: The lateral triangular faces converge at a single vertex.
• Height: The perpendicular distance from the common vertex to the base.
• Right pyramid: The vertex is directly above the center of the base.
• Naming: Pyramids are named based on the shape of their base.

5. Cylinder

Key points about cylinders:

• Definition: A cylinder is a solid with two parallel, congruent circular bases and a curved surface.
• Axis: Joins the centers of the two bases.
• Height: The perpendicular distance between the two bases.
• Right cylinder: The axis is perpendicular to the bases.
• No vertex: Cylinders do not have vertices.
• Closed cylinder: Has 3 faces (2 circular bases and 1 lateral curved face).
• Hollow cylinder: Open at both ends, consisting of only 1 lateral face.

6. Cone

Key points about cones:

• Definition: A cone is a solid with a circular base and a curved surface meeting at a common vertex.
• Axis: Connects the vertex to the center of the circular base.
• Slant height: The distance from the vertex to any point on the edge of the base.
• Height: The perpendicular distance from the vertex to the base.
• Right cone: The vertex is directly above the center of the base.

7. Sphere

Key points about spheres:

• Definition: A sphere is a solid where all points on its curved surface are equidistant from a fixed central point.
• Centre: The fixed point at the middle of the sphere.
• Radius: The distance from the centre to any point on the surface.

3.0Euler's formula

If F, V and E are the number of faces, number of vertices and number of edges of a polyhedron then F + V – E = 2

4.0Net of solid shapes

Key points about nets:

1. Definition: A net is a flat diagram that can be folded to form a hollow solid.
2. Reverse process: Opening a hollow solid results in its net.
3. Alternate name: A net is also called a layout.
4. Variety: Nets of a solid can have different shapes.