Visualizing Solid Shapes is about understanding the three-dimensional world around us. This chapter introduces you to different types of solids, their components, and how to represent them in two dimensions.
Key Concepts:
- Solid shapes: Objects that have three dimensions: length, breadth, and height. Examples include cubes, cuboids, cylinders, cones, spheres, pyramids, etc.
- Plane figures: Flat shapes like circles, triangles, squares, and rectangles form the faces of solid shapes.
- Components of a solid shape:
- Faces: Flat surfaces that enclose the solid.
- Edges: Line segments where two faces meet.
- Vertices: Points where three or more edges meet.
- Nets: A net is a flat pattern that can be folded to form a solid shape.
- Drawing solid shapes:
- Oblique sketches: Quick, freehand drawings that show the depth of the object.
- Isometric sketches: Drawings on isometric dot paper, preserving proportions.
This chapter helps you develop spatial reasoning and visualize real-world objects as geometric shapes.
Exercise 13.1
1. Identify the nets which can be used to make cubes (Cut out copies of the nets and try it):
Ans :
Nets that can be used to make cubes:
(ii), (iii), (iv), and (vi)
2. Dice are cubes with dots on each face. Opposite faces of a die always have a total of seven dots on them.
Here are two nets to make dice (cubes); the number inserted in each square indicate the number of dots in that box.
Insert suitable number in the blanks, remembering that the number on the opposite faces should total to 7.
Ans :
3. Can this be a net for a die? Explain your answer.
Ans :
No, this net cannot be folded into a die.
Reasoning:
A standard die has opposite faces adding up to 7. In this configuration, faces 3 and 6 would be opposite, which doesn’t follow the standard rule for a die.
4. Here is an incomplete net for making a cube. Complete it in atleast two different ways. Remember that a cube has six faces. How many are there in the net here? (Give two separate diagrams. If you like, you may use a squared sheet for easy manipulation).
Ans :
5. Match the nets with appropriate solids:
Ans :
(a) – (ii)
(b) – (iii)
(c) – (iv)
(d) – (i)
Exercise 13.2
1. Use isometric dot paper and make an isometric sketch for each one of the given shapes:
Ans :
2. The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid.
Ans :
3. Three cubes with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique or isometric sketch of this cuboid.
Ans :
4. Make an oblique sketch for each one of the given isometric shapes:
Ans :
5. Give (i) an oblique sketch and (ii) an isometric sketch for each of the following:
(а) A cuboid of dimensions 5 cm, 3 cm and 2 cm. (Is your sketch unique?)
(b) A cube with an edge 4 cm long.
An isometric sheet is attached at the end of the book. You could try to make on it some cubes or cuboids of dimensions specified by your friend.
Ans :
Exercise 13.3
1. What cross-sections do you get when you give a
(i) vertical cut
(ii) horizontal cut to the following solids?
(a) A brick
(b) A round apple
(c) A die
(d) A circular pipe
(e) An ice cream cone.
Ans :
| Solid | Vertical Cut | Horizontal Cut |
| (a) Brick | Rectangle | Rectangle |
| (b) Round apple | Circle | Circle |
| (c) Die | Rectangle | Square |
| (d) Circular pipe | Rectangle | Circle |
| (e) Ice cream cone | Triangle | Circle |
Exercise 13.4
1. A bulb is kept burning just right above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You may try to experiment first and then answer these questions).
Ans :
- (i) A ball: When a light source is placed directly above a ball, the shadow cast on a flat surface will be a circle
- (ii) A cylindrical pipe: The shadow of a cylindrical pipe, when the light source is directly above, will be a rectangle.
- (iii) A book: The shadow of a book, when the light source is directly above, will be a rectangle. The specific dimensions of the
2. Here are the shadows of some 3-D objects, when seen under the lamp of an overhead projector. Identify the solid(s) that match each shadow. (There may be multiple answers for these!)
Ans :
(i) A circle: A circle as a shadow can be cast by various 3D objects, including a sphere, cylinder, or cone, depending on the angle of the light source.
(ii) A square: A square shadow can be cast by a cube, cuboid, or any other object with a square face positioned perpendicular to the light source.
(iii) A triangle: A triangle as a shadow can be formed by a cone, pyramid, or a triangular prism, depending on the angle of the light source.
(iv) A rectangle: A rectangle can be the shadow of a cuboid, a book, or any other rectangular prism, depending on its orientation to the light source.
3. Examine if the following are true statements:
(i) The cube can cast a shadow in the shape of a rectangle.
(ii) The cube can cast a shadow in the shape of a hexagon.
Ans :
(i) True
(ii) False
