Viewing Sections of a Solid: 3D figures, Nets, Sections

Viewing Sections of a Solid: In geometry, we study various solid shapes. The solid geometry includes three-dimensional shapes such as cuboids, cubes, cylinders, prisms, cones, spheres, etc. These shapes are also called solids. A solid figure (\(3-D\) object) occupies a certain amount of volume. It has \(3\) dimensions, namely, length, width, and height (or depth).

Every three-dimensional shape has a top view, front view and side view. In this article, we will study the various elements and the sections of a solid body. We will also learn to build a relationship between the number of faces, vertices, and edges of solid shapes.

What are Solids?

The shapes that are measured in three dimensions are known as solid shapes or three-dimensional shapes. Solids or three-dimensional shapes are measured by their length, width, and height (or depth or thickness).

Our surroundings are full of solid shapes. These shapes are found around us daily, such as books, containers, gas cylinders, balls, ice cream cones, etc. These shapes can be compared to solid geometrical shapes, namely cuboids, cylinders, spheres, cones, etc.

Faces, Edges, and Vertices

All solid shapes have a certain number of faces, edges and vertices. Let us know each of these terms using solid shape.

Faces

Each surface of a solid shape is defined as a face. For instance, a cube has six faces. Let us have a look at the figure given above that demonstrates a face of a cube.

Vertices

Vertices are the plural form of the vertex. In a solid shape, a vertex is described as a point where two or more edges or sides or line segments connect. A sphere is an exceptional solid shape that has no vertex. Have a look at the above figure, which shows a vertex of a cube. We can easily count and say that a cube has eight vertices.

Edges

In a solid shape, an edge is described as a line joining two corners or two vertices. The given figure represents the edges of a cube. The table shown below lists some three-dimensional shapes with the details of their faces, edges and vertices.

Nets of Solids

The net of a three-dimensional solid shape is the outlines of its faces which when joined together, forms the shape. The net of a solid shape signifies its unfolded form. In other words, when the surface of a three-dimensional shape is opened up and laid out, we can examine each face as a two-dimensional shape.

For example, the nets of some solid shapes are shown below. If we open a cube, we will get six square faces.

If we open a cuboid, we will get the net of the cuboid. We will get six rectangular pieces in the net of a cuboid.

A triangular prism has three rectangular faces and two triangular faces. The net of it looks like,

A cylinder has three faces. If we split its top and bottom faces, we will get two circular faces, and if we open up its curved face, we will get a rectangle.

Different Views of Solid Shapes

When we click a photo of a solid shape or three-dimensional shape, the image appears to be two dimensional. When viewed from different viewpoints, we will get different \(2-D\) views of the same \(3-D\) shape. Every solid has mainly three different views. Let us take a three-dimensional shape and see its three different views.

1. Top View: The top view of a solid shape is the two-dimensional shaped view of an object when we see it from the top or above the object.
2. Side View: The side view of a solid shape is the two-dimensional shaped view of an object when it is observed from one of its sides.
3. Front View: The front view of an object is the two-dimensional shaped view of an object when we see it from the front side of the object.

Let us have a look at another example to understand it better. In the following image, the top, front and side views of a square hole are given.

Different Ways of Viewing Solids

We can view different sections of a solid in different ways. Let us have a look at those methods.

Viewing Solids by Cross-section Method 

Let us say we are cutting a solid shape vertically or horizontally. We can see that it produces a two-dimensional shape. This shape is called the cross-section. The shape that we get depends on the cut of the solid shape. For example, see the figure given below, in which a cylinder is cut vertically and horizontally. The horizontal cross-section looks like a rectangle, whereas a vertical cross-section seems like a circle.

Let us see few examples of cross-sections of some solids.

In the above image cross-section of a cuboid is shown.

In the above image cross-section of a triangular pyramid is shown.

Viewing Solids by Shadow Method

Viewing a \(2-D\) shadow of the solid is also a method of observing a solid shape. Let us arrange by keeping a light source just in front of a solid \(3-D\) body (cylinder) and watch the shadow obtained on the wall.
If the light source falls at the circular base, a circle is observed in the wall opposite the light source. If it falls at the curved face of the cylinders then, we will observe a rectangular shadow opposite to the light source.

Drawing Solid 3-D Shapes on a Flat Surface

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

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. To do an oblique sketch of a solid shape:

1. Draw the front view shape and the opposite shape of the front view of the object.
2. Connect the vertices or corners. 
3. Draw dotted lines in the hidden edges.

The following figure shows how a \(3-D\) shape can be drawn with oblique sketching.

Isometric Sketches

To draw an isometric sketch, we use 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.

Solved Examples – Viewing Different Sections of a Solid

Q.1. Draw the isometric sketch of the following figure.

Ans: To draw an isometric sketch, we use 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 cube.

Q.2. Look at the \(3-D\) shape given below and identify its given view.

Ans: We know that the front view of an object is the two-dimensional shaped view of an object when we see it from the front side of the object. It is visible that the given view is the front view of the object.

Q.3. Show the vertical cross-sections of a cuboid.
Ans: Here, we will cut the cuboid vertically such that the cross-sections so obtained are the two-dimensional planes, i.e., a rectangle. So, the cross-sections are shown below.

Q.4. Observe the \(3-D\) shape given below and identify its given view.

Ans: The top view of a solid shape is the two-dimensional shaped view of an object when we see it from the top or above the object. It is seen that the given view is the top view of the object.

Q.5. How many faces, vertices, and edges a triangular pyramid has?
Ans: A triangular pyramid has four faces, four vertices, six edges.

Summary

In this article, we studied solid shapes, edges, faces, and vertices of the solid shapes, examples of nets of solid shapes. Later we learned about viewing a solid shape, i.e. top view, front view and side view. In addition to this, we also learned about the cross-section view, shadow view, etc. At last, we learned to draw solid \(3-D\) shapes on a flat surface.

Learn All the Concepts on 3-D Shapes

Frequently Asked Questions (FAQs) – Viewing Different Sections of a Solid

Let’s look at some commonly asked questions about sections of solids:

Q.1. Which is a way to view a different section of a solid?
Ans: The ways to view different solid sections are by cutting a solid shape vertically or horizontally and another way to by viewing two-dimensional shadow of a solid object.

Q.2. How many views are there in a solid?
Ans: When we click a photo of a solid shape or three-dimensional shape, the image appears to be two dimensional. When viewed from different viewpoints, we will get different \(2-D\) views of the same \(3-D\) shape. Every solid has mainly three different views: Top view, side view, front view.

Q.3. What is viewing different sections of a solid?
Ans: There are two ways for viewing different sections of solid. These are:
1. Viewing the solids by cross-section method
2. Viewing the solids by shadow method

Q.4. What is the shape of the shadow of a cone?
Ans: Suppose light falls on a cone. The shadow of the solid shape forms a two- dimensional shape. When a light source falls on the apex of a cone, we get the shadow as a two-dimensional shape, which is a circle.

Q.5. What is the net of a solid?
Ans: The net of a three-dimensional solid shape is the outlines of its faces which, when joined together, forms the shape.
The net of a solid shape signifies its unfolded form.

Now you are provided with all the necessary information on viewing different sections of solids and we hope this detailed article is helpful to you. If you have any queries regarding this article, please ping us through the comment section below and we will get back to you as soon as possible.