3D shapes are nothing but solids that consist of 3 dimensions, namely  length, breadth, and height. The "D" in "3D shapes" stands for "Dimensional."
These 3D shapes occupy space and are found in our daytoday life. We touch, feel, and use them.
Let us go through this short lesson to know more about 3D shapes!
Lesson Plan
What Are 3D Shapes?
In mathematics, we study about 3dimensional objects in the concept of solids and try to apply them in real life.
We will now learn about each 3D shape in detail.
3D shapes are classified into several categories.
Some of them have curved surfaces; some are in the shape of pyramids or prisms.
Definition of 3d Shapes
Threedimensional objects having three dimensions namely length, breadth, and height.
Let us first learn about the 3dimensional shapes with curved surfaces with examples.
Sphere
 It is shaped like a ball and is perfectly symmetrical.
 Every point on the sphere is at an equal distance from the center.
 It has one face, no edges, and no vertices.
Cylinder
 It has one curved side.
 The shape stays the same from the base to the top.
 It is a threedimensional object with two identical ends that are either circular or oval.
Cone
 A cone has a circular or oval base with an apex (vertex).
 A cone is a rotated triangle.
 Based on how the apex is aligned to the center of the base, a right cone or an oblique cone is formed.
Torus
 A torus is a regular ring, shaped like a tire or doughnut.
 It is formed by revolving a smaller circle around a larger circle.
 It has no edges or vertices.
Now let us learn about the threedimensional shapes called pyramids.
Pyramid
 A pyramid is a polyhedron with a polygon base and an apex with straight lines.
 Based on its apex alignment with the center of the base, they can be classified into regular and oblique pyramids.
 A pyramid with a:
 Triangular base is called a Tetrahedron
 Quadrilateral base is called a square pyramid
 Pentagon base is called a pentagonal pyramid
 Regular hexagon base is called a hexagonal pyramid
Let's learn about the threedimensional shapes called prisms.
Prisms
 Prisms are solids with identical polygon ends and flat parallelogram sides.
 It has the same crosssection all along its length.
 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.
Next, let's learn about 3dimensional shapes with regular polyhedrons (Platonic Solids).
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
 Cube with six square faces
 They have identical faces of regular polygons.
 Rhyme to remember 3D shapes:
"3D 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.
Properties of 3D Shapes
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:
Where, radius (r)
Properties  Surface Area  Volume 


\(\pi r(r+s)\)  \( \frac{1}{3} \pi r^2h\) 
Cube:
Where, edge length (EL)
Properties  Surface Area  Volume 


\(6 \times (E L)^2\)  \((EL)^3\) 
Prism:
Where, base area (BA), perimeter (P), height (H)
Properties  Surface Area  Volume 


\(2\times (BA)\)+ \(P \times H\)  \(BA\times H\) 
Pyramid:
Where base area (BA), perimeter (P) altitude (A), and slant height (SH)
Properties  \(Surface\) \(Area\)  Volume 


\(B\:A\) + \(\frac{1}{2} \times P \times(SH)\) 
\(\frac{1}{3} \times BA \times A\) 
Faces, Edges, and Vertices
As mentioned before, 3D 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 3D Shapes
 A face refers to any single flat surface of a solid object.
 3D shapes can have more than one face.
Edges of 3D 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 3D 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:
3 D shapes  Faces  Edges  Vertices 

Sphere 
1 
0  0 
Cylinder 
2 
2  0 
Cone 
2 
2  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 
How to Make 3D Figures
We can better understand the threedimensional shapes and their properties by using nets.
A 2dimensional shape that can be folded to form a 3dimensional object is known as a geometrical net.
A solid may have different nets.
In simple words, the net is an unfolded form of a 3D figure.
Let's practice making 3D shapes using the simulations shown below.
Move the slider to see how the nets shape into threedimensional figures.
The following simulation shows 3D shapes with curved surfaces.
Move the slider and the screen to explore the view from different angles.
The next simulation shows how to create 3D shapes which have the properties of a regular polyhedron.
 Threedimensional objects have 3 dimensions namely length, breadth, and height.
 3D shapes have faces, edges, and vertices.
 Learning about 3D solids will help us in our daytoday life as most of our activities revolve and depend on them.
Solved Examples of 3D Shapes
Example 1 
A construction worker wants to build a 3D sphere using cement.
He wants to know the amount of cement required to construct the sphere of radius 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 
Megan 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 she 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, she needs roughly 425 \(in^3\) of milk to fill her glass.
\(Volume =424.11\: in^3\) 
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 cube are polyhedrons.
\(\therefore\) Egyptian Pyramids and Rubik's Cube 
Example 5 
Give a few examples of reallife objects in the shape of TORUS.
Solution
 Doughnut
 Car tires
 Ring
 Swimming tube and so on.
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
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Frequently Asked Questions (FAQs)
1. What can a 3D shape also be called?
In geometry, a threedimensional shape can also be called a solid.
2. What objects have 3D shapes?
The objects that are threedimensional with length, breadth and height defined are known as 3D Shapes.
Some of the common examples of 3D shapes are:
Dice (cube)
Shoebox (cuboid or rectangular prism)
Ice cream cone (cone)
Globe (sphere)
3. What is the volume of a 3D shape?
Volume of 3D Shapes refers to the amount of cubic space filled within the shapes.
To find the volume, we need the measurements of the three dimensions.