Visualizing Solid Shapes
As we look around, we observe that all the objects have a shape. Right from a computer to a book, everything has a unique shape. Shapes are either two-dimensional or three-dimensional. A shape that has a length and a width is called a two-dimensional shape (also known as 2-D shape) and a shape that has a length, a width and a height is called a three-dimensional shape (also known as 3-D shape).
A solid shape is a 3-D shape that has 3 dimensions, which are length, width and height (depth). In this article, we will learn about solid shapes and how to visualize them.
What are 2-D and 3-D shapes?
2-D shapes or Plane figures
2-D shapes are plane geometric figures made up of either straight or curved lines. They only have length and width (breadth). 2-D shapes do not have any depth. Circles, triangles, squares and rectangles are some examples of 2-D shapes. Shapes that are made up of three or more straight lines are referred to as 'Polygons'. Some common 2-D shapes are circle, oval, triangle, square, diamond, rhombus, parallelogram, rectangle.
3-D shapes or Solid shapes
A 3-D shape or a solid shape has a length, width and height. A solid shape occupies some space and rests on one or more surfaces. Cubes, cones, spheres, cuboids are some examples of solid shapes. Many real world objects like a book, laptop, ball, birthday cone resemble solid shapes. Some of the 3-D shapes are cuboid, sphere, cone, cylinder, pyramid, cube.
Now let us learn some important terms related to solid shapes.
What are Faces, Vertices and Edges?
All solid shapes are defined by a certain number of faces, vertices and edges. Let us understand each of these terms.
Faces:
Every single surface of a solid shape is called a face. For example, a cube has 6 faces. Observe the figure shown below that shows a face of a cuboid.
Vertices
In a solid shape, a 'Vertex' is defined as a point where two or more lines meet. Vertices is the plural form of the word 'Vertex'. A sphere is an exceptional shape which does not have a vertex. Observe the following figure which shows the vertex of a cube.
Edges
In a solid shape, an 'Edge' is defined as a line segment joining two vertices or two corners. The following figure shows the edge of a cube.
The table shown below lists some three-dimensional shapes with the details of their faces, edges and vertices.
Views of Solid Shapes
All solid shapes have a top view, a side view and a front view. Let us check out each one of them.
- Top View: The top view of a solid shape is the shape of an object when we see it from the top.
- Side View: The side view of a solid shape is the shape of an object when it is seen from one of its sides.
- Front View: The front view of an object is the shape of an object when it is seen from the front side of the object.
Observe the cube given below which shows its top, side and front view.
How to Visualize a Solid Shape?
A solid shape can be visualized in many ways. Some of them are listed below.
Visualizing a Solid Shape by Cutting It
Imagine cutting a solid shape horiozontally or vertically. We can clearly see that it resembles a 2-D shape (like a square or rectangle). This is called the 'cross-section'. The shape that we get depends upon the solid shape that is being cut. For example, observe the figure shown below, in which a cylinder is cut horizontally and vertically. The horizontal cross section resembles a rectangle, whereas a vertical cross section resembles a circle.
Visualizing an Object by Its Shadow:
Imagine that a source of light falls on a solid shape, say a cone. The shadow of the solid shape forms a 2-D shape. In the figure shown below, we observe that when a light source falls on the thinner end (top) of a cone, we get the shadow as a 2-D shape, which is a circle.
Visualizing Solid Objects by Imagining the Smallest Unit:
Conside a rubik's cube (a real life example of solid shape - cube) which has 27 small cubes in it. Each cube is of 1 unit. This means when we stack up 3 rows of 3 cubes we get a cube that has 27 small cubes each measuring 1 unit.
Nets of Solid Shapes
The net of a solid shape represents its unfolded form. In other words, when the surface of a three-dimensional shape is unfolded and laid out, we can observe each face as a two-dimensional shape. This pattern that we get is called a net. For example, the net of a cylinder is shown below. We can clearly see that there are two 2-D shapes in it. One is a circle and the other one is a rectangle.
Drawing 3-D Shapes on a Paper or a Flat Surface
We can represent a 3-D shape in a 2-D flat surface like a paper. This can be done in two ways.
Oblique Sketching:
To do an oblique sketch of a solid shape:
- Draw the front view shape and the opposite shape of the object.
- Connect the corners.
- Draw a dotted line in the hidden edges.
The following figure shows how a 3-D shape can be drawn with oblique sketching.
Isometric Sketching:
Isometric sketches are drawn on isometric dotted paper with definite measurements. The figure given below shows the isometric sketch of a cuboid in an isometric dotted paper.
Topics Related to Visualizing Solid Shapes
Check out some interesting topics related to visualizing solid shapes.
Important Topics
Solved Examples
-
Example 1: Find the solid shape that will be formed by placing the following four cubes together. Also find the dimension of the new solid shape formed.
Solution:
The new solid shape formed is a cuboid.
The length of the cuboid will be 3 + 3 + 3 + 3 = 12 units.
Width of the cuboid = 3 units
Height of the cuboid = 3 units -
Example 2: Find the number of faces, edges and vertices of the following shapes shown in the figure below.
Solution:
Sphere:
Faces: 1
Edges: 1
Vertices: 0
Cuboid:
Faces: 6
Edges: 12
Vertices: 8
Triangular pyramid:
Faces: 5
Edges: 9
Vertices: 6
Square pyramid:
Faces: 5
Edges: 8
Vertices: 5
Faq's on Solid Shapes
What are Solid Shapes?
Solid shapes are 3-D shapes that have a length, width and a height (depth). Cubes, cones, spheres, cuboids are some examples of solid shapes.
What is a Face, Vertex and Edge?
The flat surface of a solid shape is called a face. The line segment joining two faces of a solid shape is called an edge. The point or corners where edges meet is called a vertex.
Does a 2-D shape have faces, vertices and edges?
No, 2-D shapes have only vertices. For example, a triangle has 3 vertices and a square has 4 vertices.
What Are the Different Views of Solid Shapes?
There are different views of solid shapes:
- Top View: The top view of a solid shape is the shape of an object when we see it from the top.
- Side View: The side view of a solid shape is the shape of an object when it is seen from one of its sides.
- Front View: The front view of an object is the shape of an object when it is seen from the front side of the object.
How Can Solid Shapes be Visualized?
Solid shapes can be visualized in the following ways:
- By cutting or slicing them horizontally or vertically.
- By passing light on a solid shape.
- By imagining the smallest unit of which a solid shape is made.
Can Solid Shapes be Drawn on Flat Surfaces?
Yes, solid shapes can be drawn on flat surfaces by using the oblique sketching technique or the isometric sketching technique.