3D Shapes

3D shapes are solids that consist of 3 dimensions - length, breadth (width), and height. 3D in the word 3D shapes means three-dimensional. Every 3D geometric shape occupies some space based on its dimensions and we can see many 3D shapes all around us in our day-to-day life. Some examples of 3D shapes are cube, cuboid, cone, and cylinder.

1.	What are 3D Shapes?
2.	Types of 3D Shapes
3.	Properties of 3D Shapes
4.	3D Shapes Formulas
5.	3D Shapes - Faces, Edges, Vertices
6.	3D Shapes Nets
7.	FAQs on 3D Shapes

What are 3D Shapes?

3D shapes are solid shapes or objects that have three dimensions (which are length, width, and height), as opposed to two-dimensional objects which have only a length and a width. Other important terms associated with 3D geometric shapes are faces, edges, and vertices. They have depth and so they occupy some volume. Some 3D shapes have their bases or cross-sections as 2D shapes. For example, a cube has all its faces in the shape of a square. Let us now learn about each 3-dimensional shape (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.

Real-Life Examples of 3D Geometric Shapes

In mathematics, we study 3-dimensional objects in the concept of solids and try to apply them in real life. Some real-life examples of 3D shapes are shown below which are a soccer ball, a cube, a bucket, and a book.

Real Life Examples of 3D Shapes - ball, cube, bucket, book

Types of 3D Shapes

There are many 3 dimensional shapes (3D shapes) that have different bases, volumes, and surface areas. Let us discuss each one of them.

Sphere

A sphere is round in shape. It is a 3D geometric shape that has all the points on its surface that are equidistant from its center. Our planet Earth resembles a sphere, but it is not a sphere. The shape of our planet is a spheroid. A spheroid resembles a sphere but the radius of a spheroid from the center to the surface is not the same at all points. Some important characteristics of a sphere are as follows.

It is shaped like a ball and is perfectly symmetrical.
It has a radius, diameter, circumference, volume, and surface area.
Every point on the sphere is at an equal distance from the center.
It has one face, no edges, and no vertices.
It is not a polyhedron since it does not have flat faces.

Sphere - 3D shape

Cube and Cuboid

Cube and cuboid are three-dimensional shapes (3D shapes) that have the same number of faces, vertices, and edges. The main difference between a cube and a cuboid is that in a cube, all its six faces are squares and in a cuboid, all its six faces are rectangles. A cube and a cuboid occupy different volumes and have different surface areas. The length, width, and height of a cube are the same, while for a cuboid, length, height, and width are different.

Cylinder

A cylinder is a 3D shape that has two circular faces, one at the top and one at the bottom, and one curved surface. A cylinder has a height and a radius. The height of a cylinder is the perpendicular distance between the top and bottom faces. Some important features of a cylinder are listed below.

It has one curved face.
The shape stays the same from the base to the top.
It is a three-dimensional object with two identical ends that are either circular or oval.
A cylinder in which both the circular bases lie on the same line is called a right cylinder. A cylinder in which one base is placed away from another is called an oblique cylinder.

Cylinder - a 3d geometric shape

Cone

A cone is another three-dimensional shape (3D shape) that has a flat base (which is of circular shape) and a pointed tip at the top. The pointed end at the top of the cone is called 'Apex'. A cone also has a curved surface. Similar to a cylinder, a cone can also be classified as a right circular cone and an oblique 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.
A cone in which the apex (or the pointed tip) is perpendicular to the base is called a right circular cone. A cone in which the apex lies anywhere away from the center of the base is called an oblique cone.
A cone has a height and a radius. Apart from the height, a cone has a slant height, which is the distance between the apex and any point on the circumference of the circular base of the cone.

Cone - a 3d geometric shape

Torus

A torus is a 3D shape. It is formed by revolving a smaller circle of radius (r) around a larger circle with a bigger radius (R) in a three-dimensional space.

A torus is a regular ring, shaped like a tire or doughnut.
It has no edges or vertices.

Torus - a 3d geometric shape

Pyramid

A pyramid is a polyhedron with a polygon base and an apex with straight edges and flat faces. Based on their 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.
A pyramid with a quadrilateral base is called a square pyramid.
A pyramid with the base of a pentagon is called a pentagonal pyramid.
A pyramid with the base of a regular hexagon is called a hexagonal pyramid.

3d shapes - Types of Pyramids

Prisms

Prisms are solids with identical polygon ends and flat parallelogram sides. Some of the characteristics of a prism are:

It has the same cross-section all along its length.
The different types of prisms are - triangular prisms, square prisms, pentagonal prisms, hexagonal prisms, and so on.
Prisms are also broadly classified into regular prisms and oblique prisms.

3D shapes - Types of Prisms

Now, let us learn about 3-dimensional shapes that are platonic solids.

Polyhedrons

A polyhedron is a 3D shape that has polygonal faces like (triangle, square, hexagon) with straight edges and vertices. It is also called a platonic solid. There are five regular polyhedrons. A regular polyhedron means that all the faces are the same. For example, a cube has all its faces in the shape of a square. Some more examples of regular polyhedrons are given below:

A Tetrahedron has four equilateral-triangular faces.
An Octahedron has eight equilateral-triangular faces.
A Dodecahedron has twelve regular pentagon faces.
An Icosahedron has twenty equilateral-triangular faces.
A Cube has six square faces.

Regular Polyhedrons - 3d geometric shapes

Properties of 3D Shapes

Every 3D shape has some properties which help us to identify them easily. Let us discuss each of them briefly.

3D Shapes	Properties
Sphere (With radius - r)	It has no edges or vertices (corners). It has one curved surface. It is perfectly symmetrical. All points on the surface of a sphere are at the same distance (r) from the center.
Cylinder	It has a flat base and a flat top. The bases are always congruent and parallel. It has one curved side.
Cone	It has a flat base. It has one curved side and one-pointed vertex at the top or bottom known as the apex.
Cube	It has six faces in the shape of a square. The sides are of equal lengths. 12 diagonals can be drawn on a cube.
Cuboid	It has six faces which are rectangular in shape. All the sides of a cuboid are not equal in length. 12 diagonals can be drawn on a cuboid.
Prism	It has identical ends (polygonal) and flat faces. It has the same cross-section all along its length.
Pyramid	A Pyramid is a polyhedron with a polygon base and an apex with straight lines. Based on their apex alignment with the center of the base, they can be classified into regular and oblique pyramids.

3D Shapes Formulas

As discussed, all 3 Dimensional shapes have a surface area and volume. The surface area is the area covered by the 3D shape at the bottom, top, and all the faces including the curved surfaces, if any. Volume is defined as the amount of space occupied by a 3D shape. Every three-dimensional shape (3D shape) has different surface areas and volumes. The following table shows different 3D shapes and their formulas.

3D Shape	Formulas
Sphere	Diameter = 2 × r; (where 'r' is the radius) Surface Area = 4πr² Volume = (4/3)πr³
Cylinder	Total Surface Area = 2πr(h+r); (where 'r' is the radius and 'h' is the height of the cylinder) Volume = πr²h
Cone	Curved Surface Area = πrl; (where 'l' is the slant height and l = √(h² + r²)) Total Surface Area = πr(l + r) Volume = (1/3)πr²h
Cube	Lateral Surface Area = 4a²; (where 'a' is the side length of the cube) Total Surface Area = 6a² Volume = a³
Cuboid	Lateral Surface Area = 2h(l + w); (where 'h' is the height, 'l' is the length and 'w' is the width) Total Surface Area = 2 (lw + wh + lh) Volume = (l × w × h)
Prism	Surface Area = [(2 × Base Area) + (Perimeter × Height)] Volume = (Base Area × Height)
Pyramid	Surface Area = Base Area + (1/2 × Perimeter × Slant Height) Volume = [(1/3) × Base Area × Altitude]

3D Shapes - Faces Edges Vertices

As mentioned earlier, 3D shapes and objects are different from 2D shapes and objects because of the presence of the three dimensions - length, width (breadth), and height. As a result of these three dimensions, these objects have faces, edges, and vertices. Observe the figure given below to identify the face, vertex, and edge of a 3D shape.

3D Shapes - Faces Edges and Vertices

Faces

A face refers to any single flat or curved surface of a solid object.
3D shapes can have more than one face.

Edges

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

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.

The following table shows the faces, edges, and vertices of a few 3-dimensional shapes (3D shapes).

3D shapes	Faces	Edges	Vertices
Sphere	1	0	0
Cylinder	3	2	0
Cone	2	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	4
Pentagonal Pyramid	6	10	6
Hexagonal Pyramid	7	12	7

3D Shapes Nets

We can understand the three-dimensional shapes and their properties by using nets. A 2-dimensional shape that can be folded to form a 3-dimensional 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. Observe the following figure to see the nets that are folded to make a 3D shape.

3D Shapes Nets

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3D Shapes Worksheet

Worksheet on 3D Shapes

3D Shapes Examples

Example 1: State true or false using the properties of 3D shapes.

a.) 3D shapes are solid shapes or objects that usually have three dimensions - length, width, and height.

b.) 3D shapes are also called solid shapes.

c.) A 2d shape that can be folded to form a 3-dimensional object is known as a geometrical net.

Solution:

a.) True, 3D shapes are solid shapes or objects that usually have three dimensions - length, width, and height.

b.) True, 3D shapes are also called solid shapes.

c.) True, a 2d shape that can be folded to form a 3-dimensional object is known as a geometrical net.
Example 2: Find the surface area of a cuboid of length 3 units, width 4 units, and height 5 units.

Solution:

Given that, length of the cuboid = 3 units, width of the cuboid = 4 units, height of the cuboid = 5 units

Surface area of the cuboid is 2 × (lw + wh + lh) square units
= 2 × (lw + wh + lh)
= 2[(3 × 4) + (4 × 5) + (3 × 5)]
= 2(12 + 20 + 15)
= 2(47)
= 94 square units.
Therefore, the surface area of the cuboid is 94 square units.
Example 3: Megan wants to drink milk from a glass that is in the shape of a cylinder. The height of the glass is 15 units and the radius of the base is 3 units. What is the quantity (volume) of milk that she requires to fill the glass completely?

Solution:

Given that, the height of the glass = 15 units and the radius of the base = 3 units.

To find the volume of the glass, we need to use the formula for the volume of a cylinder, which is πr²h cubic units.

The volume of the glass, V = πr²h
V = π × (3²) × 15
V = π × 135
V = 423.9 cubic units.

Therefore, she needs approximately 424 cubic units of milk to fill her glass.

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Practice Questions on 3D Shapes

FAQs on 3D Shapes

What are 3D Shapes?

A shape or a solid that has three dimensions is called a 3D shape. 3D shapes have faces, edges, and vertices. They have a surface area that includes the area of all their faces. The space occupied by these shapes gives their volume. Some examples of 3D shapes are cube, cuboid, cone, cylinder. We can see many real-world objects around us that resemble a 3D shape. For example, a book, a birthday hat, a coke tin are some real-life examples of 3D shapes.

What is a Face, Edge, and a Vertex in a 3D Shape?

A very important feature of a 3D shape is its face, vertex, and edge. Generally, the face of a 3D shape is a polygon-shaped flat surface. A 3D shape has more than one face except for a sphere. A vertex is a sharp-pointed corner. Edge is a line segment or the distance between two adjacent vertices of a 3D shape. Different 3D shapes have different numbers of faces, vertices, and edges. For example, a cube is a 3D shape that has 6 faces, 12 edges, and 8 vertices.

Does a 3D Geometric Shape Only Have a Flat Surface?

No, a 3D shape may have flat surfaces as well as curved surfaces. For example, a cone and a cylinder, have flat surfaces of a circle as well as curved surfaces.

What is the Difference Between 2D and 3D Shapes?

The differences between a 2D shape and a 3D shape are given as follows.

2D shapes have a length and a width, whereas, 3D shapes have a length, a width, and a height.
2D shapes have an area, they do not occupy any volume, whereas 3D shapes have a surface area and a volume.
Examples of 2D shapes are triangle, square, rectangle, and examples of 3D shapes are cube, cuboid, prism.

What is the Surface Area and Volume of a 3D Shape?

Surface area means the area of all the individual faces of the 3D shape. All the 3D shapes have some depth. The space inside a 3D shape is called its volume.

What is the Difference Between Lateral Surface Area and Curved Surface Area of a 3D Shape?

Lateral surface area means the area of all the surfaces of the 3D shape excluding the top and the bottom surfaces. The curved surface area includes the area of only the curved surface in a 3D shape. For example, a cube has 6 flat faces. Its lateral surface area includes the area of all 4 faces excluding the top and the bottom face. A cylinder has two flat faces and one curved surface. So its curved surface area is the area of the curved part between the top and bottom faces which are circular in shape.

Which 3D Shape has No Flat Face, Edge, or Vertex but Only One Curved Surface?

A sphere is a 3D shape that has no flat face, edges, or vertices. It has only one curved surface. The surface area of a sphere is calculated with the help of the formula, Surface area of sphere = 4πr². A torus is another shape that does not have a flat face, edge, or vertex. It is in the shape of a ring. It is formed by revolving a smaller circle around a larger circle in a three-dimensional space.

What are the Common Properties of 3D Geometric Shapes?

The common properties of 3D shapes are as follows.

3D shapes have a length, width, and height. A sphere is exceptional as it does not have these three dimensions, but it extends in three directions.
3D shapes may or may not have faces, vertices, edges, and curved surfaces.
The faces of most of the 3D shapes are polygons like a triangle, square, rectangle.

What can a 3D Shape also be Called?

In geometry, a three-dimensional shape can also be called a solid shape.

What Objects are 3D Shapes?

The objects that are three-dimensional with length, breadth, and height defined are known as 3D Shapes. A few examples of 3D shapes are a dice which is in the form of a cube, a shoe box which is in the form of a cuboid or rectangular prism, an ice cream cone which is in the form of a cone, a globe which is in the form of a sphere.

What is the Volume of a 3D Shape?

The volume of 3D Shapes refers to the amount of cubic space filled within the shapes. To find the volume, we need the measurement of the three dimensions. The calculations of the volume of 3D shapes become easier if we know the formula of each shape.

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