Visualising Solid Shapes: We are aware of the plane shapes and solid shapes. Plane shapes have two measurements like length and breadth and thus are known as \(2 – D\) shapes. A solid figure (\(3 – D\) object) occupies a certain amount of volume. It has \(3\) dimensions, namely, length, width, and height (or depth).

Triangles, rectangles, rhombus, parallelogram, etc., are \(2 – D\) figures while cube, cuboid, prism, polyhedron, etc., are \(3 – D\) shapes.

Here, we will study the various elements of a solid body. We will also learn to name and match different solid objects around us. We will also learn to establish a relationship between the number of faces, vertices, and edges of \(3 – D\) shapes.

What are Shapes?

Everything we see around us has a shape. We can define a shape as the boundary or outline of an object. Most objects that we see or touch have one thing in common. They all occupy space. The shape of an object does not depend on the size or colour of the object.

Faces, Edges, and Vertices

Some of the basic \(3 – D\) shapes are cubes, cuboids, cylinders, cones, and spheres. The three main parts of a \(3 – D\) body are faces, edges and vertices. The face is a flat surface of a \(3 – D\) solid. Edge is a line where two faces of a \(3 – D\) object meet, and vertex is a corner where the edges of a solid meet. Thus, the main elements of a solid are faces, edges, and vertices.

Counting Faces, Edges, and Vertices of Polyhedron

A polyhedron is a solid in three dimensions with flat polygonal faces, straight edges, and sharp vertices or corners in elementary geometry.

Cuboid: Cuboid is a solid or hollow body with \(6\) rectangular faces with adjacent faces at the right angle to each other and opposite faces parallel to each other. A cuboid has length, breadth, and height of different dimensions.

The given figure shows a cuboid, and by observing the above formation, we can say that a cuboid has;
1. \(6\) faces, namely, \(ABCD,\,ABFE,\,AEHD,\,CGHD,\,CGFB\) and \(EFGH.\)
2. \(12\) edges, namely, \(AB,\,BC,\,CD,\,DA,\,AE,\,EH,\,HD,\,EF,\,FG,\,GH,\,BF\) and \(CG.\)
3. \(8\) vertices, namely, \(A,\,B,\,C,\,D,\,E,\,F,\,G\) and \(H.\)

Cube: A cube is a symmetrical \(3 – D\) shape, either hollow or solid, contained by \(6\) equal squares. A cube is a type of cuboid with all sides equal, i.e., \({\rm{length}} = {\rm{breadth}} = {\rm{height}}.\) Each face of a cube is a square in shape, and all the 6 faces of a cube are equal. And, since a cube is a cuboid, it also has;

1. \(6\) faces, namely, \(ABCD,\,ABFE,\,AEHD,\,CGHD,\,CGFB\) and \(EFGH.\)
2. \(12\) edges, namely, \(AB,\,BC,\,CD,\,DA,\,AE,\,EH,\,HD,\,EF,\,FG,\,GH,\,BF\) and \(CG.\)
3. \(8\) vertices, namely, \(A,\,B,\,C,\,D,\,E,\,F,\,G\) and \(H.\)

Cylinder: A cylinder is a solid or a hollow geometrical figure with a curved side and two identical circular flat ends. A cylinder is a \(3 – D\) figure with no vertex, \(2\) edges, and \(3\) faces.

Sphere: A sphere is a round solid or hollow figure, with every point on its surface equidistant from its centre. A sphere is a \(3 – D\) figure with \(0\) vertexes, \(0\) edges, and \(1\) surface, which is a curved surface.

Cone: A cone is a solid or hollow object that tapers from a circular base to a point. Cone is a \(3 – D\) figure with \(1\) vertex, \(1\) edge, and \(2\) surfaces.

Prism: A prism is a solid geometrical figure whose two ends are similar, equal, and parallel rectilinear figures whose side-faces are parallelograms or rectangles. Based on the type of prism, the number of its faces, edges, and vertices varies.
The number of faces, edges, and vertices of some of the \(3 – D\) shapes are summarised below in the table.

Different Views of Solid Shapes

When we take a photo of a \(3 – D\) shape, the image appears to be a \(2 – D.\) When viewed from different angles, we will get different \(2 – D\) views of the same \(3 – D\) shape. Every object has mainly \(3\) different views:
1. Top View
2. Side View
3. Front View

If you ask a person to make a box with wood, it will be easy for him to make the box if we draw and give him the top view, the side view, and the front view.

The following photos show different views of a \(3 – D\) pack of chocolates.

Also, if we sketch the views by outlining the edges, they will look like as;

Different Ways of Viewing 3-D Shapes

We can see a solid \(3 – D\) shape from different angles like the top view, side view, and front view. While viewing a \(3 – D\) object, we may not be able to see all its parts. We can visualise the hidden features from different viewpoints. We can view different sections of a solid in different ways. Let us have a look at those methods.

1. Cross-section Method: We can visualise the cross-section of a solid in different ways. For example, we can see a cuboid by cutting it, which results in the cross-section of the cuboid. Here, we will cut the cuboid vertically such that the cross-section so obtained is a plane, i.e., a rectangle.

We can cut it horizontally as well. In this case, also, we get the cross-section of the cuboid, i.e., a rectangle.

2. Viewing Shadow: Viewing a \(2 – D\) shadow of the solid is also a way of observing a solid shape. Let us arrange by keeping a torch just in front of a solid \(3 – D\) body and watch the shadow obtained on a screen.

Drawing Solid 3-D shapes on a Flat Surface

To draw a solid shape on paper, we can use various techniques.

1. Oblique Sketches: In an oblique sketch, our motive is to draw a \(3 – D\) shape on paper such that the image looks like the given \(3 – D\) shape. Its size can be bigger or smaller than the originally given \(3 – D\) shape, but still, we can recognize it as a solid \(3 – D\) shape. Such sketches of \(3 – D\) solids are called oblique sketches. For example, see the oblique sketch of a cuboid below.

2. Isometric Sketches: To draw an isometric sketch, we use a special sheet of paper called an isometric sheet. The isometric sheet has dots marked at equal measurements. The sides drawn on an isometric sheet have the exact size and shape of the given solid \(3 – D\) body. Below given are the isometric sketches of a cuboid and a cube.

Solved Examples – Visualising Solid Shapes

Q.1. Draw the top view, front view, and side view of the given following shape.

Ans: The top view, front view, and the side view of the following shape is as follows:

Q.2. Look at the \(3 – D\) shape given below. Draw its views when it is seen from front, top, and side.

Ans:

Q.3. Draw an oblique sketch of a cube with sides \(4\,{\rm{cm}} \times 4\,{\rm{cm}} \times 4\,{\rm{cm}}{\rm{.}}\)
Ans: Take a squared graph paper.

Draw the front face of the cube.

Draw the opposite face of the same size as that of the front face.

Join the corresponding corners

Draw the figure again with the hidden edges in the dotted line.

Q.4. The below-given figure shows an object formed by metal cubes of the same size. Draw its top view, front view, and side view.

Ans: The top view, front view, and the side view of the following shape is shown below;

Q.5. Write the number of edges, faces, and vertices of a cylinder.
Ans: A cylinder has \(2\) edges, \(3\) faces and \(0\) vertices.

Summary

In this article, we learned about solid shapes, starting from the definition of solids, then learning about the edges, faces and vertices of the solid bodies. Later we learned about viewing a solid shape, i.e. top view, front view and side view. In addition to this, we also learned to draw solid \(3 – D\) shapes on a flat surface.

Learn All Concepts on Shapes and Angles

Frequently Asked Questions – Visualising Solid Shapes

Q.1. What are solid shapes with examples?
Ans: We can define a solid shape as the boundary or outline of an object. A solid shape has a length, breadth, and height and is generally referred to as \(3 – D\) shapes. Some examples of solid shapes are cube, cuboid, cone, prism, etc.

Q.2. How do you visualise solids?
Ans: When we take a photo of a \(3 – D\) shape, the image appears to be a \(2 – D.\) When viewed from different angles, we will get different \(2 – D\) views of the same \(3 – D\) shape. Every object has mainly \(3\) different views:
1. Top View
2. Side View
3. Front View

Q.3. What are the major types of solid shapes?
Ans: The major types of solid shapes are cube, cuboid, sphere, cylinder, cone, prism, pyramid, etc.

Q.4. What is visualising solid shape?
Ans: Visualising a solid shape means viewing it from its front, side, or top view.

Q.5. Explain the methods to draw a solid \(3 – D\) shape on a flat surface.
Ans: To draw a solid shape on paper, we can use various techniques.
1. Oblique Sketches: In an oblique sketch, our motive is to draw a \(3 – D\) shape on paper such that the image looks like the given \(3 – D\) shape. Its size can be bigger or smaller than the original given \(3 – D\) shape, but still, we can recognise it as a solid \(3 – D\) shape. Such sketches of \(3 – D\) solids are called oblique sketches.
2. Isometric Sketches: To draw an isometric sketch, we use a special sheet of paper called an isometric sheet. The isometric sheet has dots marked at equal measurements. The sides drawn on an isometric sheet have the exact size and shape of the given solid \(3 – D\) body.

We hope you find this detailed article on visualising solid shapes helpful. If you have any queries or doubts regarding this topic, ask them in the comment section. We will assist you at the earliest. Happy learning!