Solid shapes are nothing but solids that consist of 3 dimensions, namely length, breadth, and height. Solid shapes are also known as 3D shapes.
These solid shapes occupy space and are found in our daytoday life. We touch, feel, and use them.
In this fun lesson, you can check out some interactive simulations to know more and try your hand at solving a few interesting practice questions at the end of the page. So, what are you waiting for?
Let us go through this short lesson to know more about solid shapes!
Lesson Plan
What Are Solid Shapes?
In mathematics, we study shapes and their different types and try to apply them in real life.
We will now learn about each solid shape in detail.
Solid shapes are classified into several categories.
Some of them have curved surfaces; some are in the shape of pyramids or prisms.
Definition of Solid Shapes
Solid shapes are threedimensional shapes that have length, breadth, and height as the three dimensions.
Let us first learn about solid shapes with curved surfaces with examples.
Different Solid Shapes With Their Properties
Sphere
Where, radius (r)
Properties  Surface Area  Volume 


\(4\pi r^2\)  \(\frac{4}{3}\pi r^3\) 
Cylinder
Where radius (r), height (h)
Properties  Surface Area  Volume 


\(2\pi r(r+h)\)  \(\pi r^2h\) 
Cone
 Based on how the apex is aligned to the center of the base, a right cone or an oblique cone is formed.
Where, radius (r)
Properties  Surface Area  Volume 


\(\pi r(r+s)\)  \( \frac{1}{3} \pi r^2h\) 
Pyramid
 A pyramid with a:
 Triangular base is called a Tetrahedron
 A quadrilateral base is called a square pyramid
 Pentagon base is called a pentagonal pyramid
 Regular hexagon base is called a hexagonal pyramid
Where base area (BA), perimeter (P) altitude (A), and slant height (SH)
Properties  Surface Area  Volume 


\(B\:A\) + \(\frac{1}{2} \times P \times(SH)\) 
\(\frac{1}{3} BA^2\) 
Prisms
 The different types of prisms are triangular prisms, square prisms, pentagonal prisms, hexagonal prisms, etc.
 Prisms are also broadly classified into regular prisms and oblique prisms.
Where, base area (BA), perimeter (P), height (H)
Properties  Surface Area  Volume 


\(2\times (BA)\)+ \(P \times H\)  \(BA\times H\) 
Polyhedrons/Platonic Solids
 There are five polyhedrons.
 Tetrahedron with four equilateraltriangular faces
 Octahedron with eight equilateraltriangular faces
 Dodecahedron with twelve pentagon faces
 Icosahedron with twenty equilateraltriangular faces
 Hexahedron or cube with six square faces.
 They have identical faces of regular polygons.
Where, edge length (EL)
Properties of Cube  Surface Area  Volume 


\(6 \times (E L)^2\)  \((EL)^3\) 
 Rhyme to remember solid shapes:
"Solid shapes are fat, not flat.
Find a cone in a birthday hat!
You see a sphere in a basketball,
And a cuboid in a building so tall!
You see a cube in the dice you roll,
And a cylinder in a shiny flag pole!" 
Moving your fingers along geometric solids will help you understand the concept of faces, edges, and vertices.
Faces, Edges, and Vertices of Solid Shapes
As mentioned before, solid shapes and objects are different from 2D shapes and objects because of the presence of the three dimensions  length, breadth, and height.
As a result of these three dimensions, these objects have faces, edges, and vertices.
Let's understand these three in detail.
Faces of Solid Shapes
 A face refers to any single flat surface of a solid object.
 Solid shapes can have more than one face.
Edges of Solid Shapes
 An edge is a line segment on the boundary joining one vertex (corner point) to another.
 They serve as the junction of two faces.
Vertices of Solid Shapes
 A point where two or more lines meet is called a vertex.
 It is a corner.
 The point of intersection of edges denotes the vertices.
For example:
Solid Shapes  Faces  Edges  Vertices 

Sphere 
1 
0  0 
Cylinder 
2 
2  0 
Cone 
1 
1  1 
Cube 
6 
12  8 
Rectangular Prism 
6 
12  8 
Triangular Prism 
5  9  6 
Pentagonal Prism 
7  15  10 
Hexagonal Prism 
8  18  12 
Square Pyramid 
5  8  5 
Triangular Pyramid 
4 
6  6 
Pentagonal Pyramid 
6  10  6 
Hexagonal Pyramid 
7  12  7 
 Solids or threedimensional objects have 3 dimensions, namely length, breadth, and height.
 Solid shapes have faces, edges, and vertices.
 Learning about solid shapes will help us in our daytoday life as most of our activities revolve around and depend on them.
Solved Examples
Example 1 
A construction worker wants to build a solid sphere using cement.
He wants to know the amount of cement required to construct a sphere of radius of 10 inches.
Find the volume of the sphere using the given radius.
Solution
Given,
The radius of the sphere (r) = 10 inches
We know the formula for the volume of a sphere:
\(\begin{align}v=\frac{4}{3}\pi\ r^3 \end{align}\) 
The volume of the cement sphere \(v=\frac{4}{3}\pi\ r^3\)
Substituting the value of the radius in the above formula, we get:
\(v=\frac{4}{3}\pi\ r^3\)
\(v=\frac{4}{3}\pi (10)^3\)
\(v= 4188.8 \:inches^3\)
\(\therefore\) Volume of the cement sphere is \(4188.8\: inches^3\) 
Example 2 
Find the surface area of a cuboid of length 3 inches, breadth 4 inches, and height 5 inches.
Solution
Given that,
Length of the cuboid = 3 inches
Breadth of the cuboid = 4 inches
Height of the cuboid = 5 inches
Surface area of the cuboid is
\(\begin{align}2 \times (lb + bh + lh) \end{align}\) 
\(= 2 \times (lb + bh + lh)\)
\(= 2(3\times 4 + 4 \times 5+ 3\times 5\))
\( = 2(12+20+15\))
\(=2(47)\)
\(=94 \: inches ^2\)
\(\therefore\) Surface area of cuboid = \(94\: inches^2\) 
Example 3 
Peter wants to drink milk in a glass which is in the shape of a cylinder.
The height of the glass is 15 inches and the radius of the base is 3 inches.
What is the quantity (volume) of milk that he requires to fill the glass?
Solution
Given that,
Height of the glass = 15 inches
Radius of the glass base = 3 inches
To find the volume of the glass, we need to use the formula for the volume of a cylinder, which is
\(\begin{align}\pi r^2h \end{align}\) 
The volume of the glass, V = \(\pi r^2h\)
\(V= \pi (3)^2 \times 15\)
\(V= \pi (135)\)
\(V= 424.11\:cm^3\)
Therefore, he needs roughly 425 \(in^3\) of milk to fill his glass.
\(\therefore\) \(Volume =424.11\: in^3\) 
Example 4 
Identify the regular polyhedron from the images shown below.
Solution
Regular polyhedrons include:
 Prisms
 Pyramids
 Platonic solids
The given examples of polyhedron must come under these categories.
Thus, the Egyptian pyramids and Rubik's cubes are polyhedrons.
\(\therefore\) Egyptian Pyramids and Rubik's Cube 
Interactive Questions
Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.
Let's Summarize
We hope you enjoyed learning about solid shapes with the simulations and interactive questions. Now you will be able to easily solve problems on different types of solid shapes.
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Frequently Asked Questions (FAQs)
1. What is a solid shape?
The objects that are threedimensional with length, breadth, and height defined are known as solid shapes.
2. What can a solid shape also be called?
In geometry, a solid shape can also be called a threedimensional shape.
3. What are the different solid shapes?
The different solid shapes are cube, cuboid, sphere, prism, cylinder, and pyramid, etc.
4. What is the volume of a solid shape?
The volume of solid shapes refers to the amount of cubic space filled within the shapes.
To find the volume, we need the measurements of the three dimensions.
5. Is a sphere solid or flat shape?
A sphere is a solid shape with no edges or vertices (corners).
6. What is a solid triangle called?
A solid triangle is called a triangular prism.
7. How many faces does a cube have?
A cube has 6 faces.
8. How many edges does a cone have?
A cone has 2 edges.
9. How many vertices does a cuboid have?
A cuboid has 8 vertices.
10. How many faces does a tetrahedron have?
A tetrahedron has four equilateraltriangular faces.