CBSE Class 7 Maths Notes Chapter 15 Visualising Solid Shapes

CBSE Class 7 Maths Notes Chapter 15: These free PDF notes encourage young brains to explore the fascinating world of three-dimensional objects by acting as treasure maps. This chapter reveals the mysteries of seeing and comprehending solid shapes, from cubes to cylinders.

CBSE Class 7 Maths Notes Chapter 15 PDF

CBSE Class 7 Maths Notes Chapter 15 PDF

CBSE Class 7 Maths Notes Chapter 15 Visualising Solid Shapes

Dimensions

• A dimension is a length along a direction that can be measured.
• Length, breadth, or height (or depth) are the three dimensions.
• A point has no dimensions.
• There are one-dimensional, two-dimensional, and three-dimensional figures depending on how many dimensions they have.

1D and 2D figures

Solid Shapes

• Solid shapes have length, breadth or width, and depth or height.
• They are called 3D or three-dimensional shapes.
• Example: Cuboids, Cylinders, Spheres and Pyramids.

Perspectives of a Solid Shape

Visualising solid shapes

Visualising solid objects by viewing the smallest unit

Viewing sections of a solid by slicing or cutting

Viewing sections of a solid by using shadows

• Shadows can be used to view 3D objects as 2D shapes.
• Example: The shadows of a cylinder are shown below.

Different views of a Solid

Quantities Associated with a Solid

Faces, edges and vertices

Nets of Solid Shapes

Building 3-D objects

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Representing 3D Shapes on Paper

Drawing solids on a flat surface

• Paper is a 2D flat surface that can be used to represent solid shapes.
• To create the illusion of three dimensions, slanted sketches are created. This is referred to as a 2D solid's representation in 3D.

Obliques sketches

• Oblique sketches do not have the exact length of a solid shape but appear exactly like the solid shape.
• Example: Drawing an oblique sketch of a cube:

  Step 1 : Draw the front and the opposite faces.

  Step 2: Join the corresponding corners. (Figure 1)

  Step 3: Redraw using dotted lines for hidden edges. (Figure 2)

Isometric sketches

• Isometric sketches have measurements equal to that of the solid.
• They are usually drawn on an isometric dotted paper.
• Example: Drawing an isometric sketch of a cuboid of dimensions 4 $\times$ 3 $\times$ 3:

Step 1: Draw a rectangle to show the front face of the cuboid.

Step 2: Draw four parallel line segments of length three starting from the four corners of the rectangle.

Step 3: Connect the corresponding corners using appropriate line segments.

Step 4: The figure thus obtained is the isometric sketch of the cuboid.