Three Dimensional Shapes (3D Shapes)

What Are Three Dimensional Shapes?

In geometry, a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height. Unlike two dimensional shapes, three-dimensional shapes have height, which is the same as thickness or depth. Three dimensional is also written as 3D and hence, these figures are commonly called 3D shapes too. All three dimensional figures occupy space, which is measured in terms of volume.

Examples of Three Dimensional Shapes

A cube, rectangular prism, sphere, cone, and cylinder are the basic three dimensional figures we see around us. 

Real-life Examples of Three Dimensional Shapes

3D shapes can be seen all around us. We can see a cube in a Rubik’s Cube and a die, a rectangular prism in a book and a box, a sphere in a globe and a ball, a cone in a carrot and an ice cream cone, and a cylinder in a bucket and a barrel around us. 

Attributes of Three Dimensional Shapes

There are three attributes of a three dimensional figure: face, edge, and vertex. Let’s understand three dimensional shapes and their properties in detail.

Face: Each single surface, flat or curved, of the 3D figure is called its face.

Edge: The line, where two faces of the 3D figures meet, is called its edge.

Vertex: Each corner, where three faces of 3D figures meet, is called its vertex. Vertices are the plural of the vertex.

List of Three Dimensional Shapes

Here’s a list of the names of three dimensional shapes with their pictures, and attributes.

Formula of Three Dimensional Shapes

Net of Three Dimensional Shapes

A net is a pattern made when the surface of a 3D figure is laid out flat, showing each face of the figure.

3D figures can have more than one net pattern. A few 3D shapes names and their nets are shown below:

Fun Facts:
All three dimensional shapes are made up of two dimensional shapes.

Difference between 2D Shapes and 3D Shapes

Let’s differentiate between 2D and 3D shapes by understanding two dimensional and three dimensional shapes and their properties.

Solved Examples

Example 1: Which of the following is a 3D shape?

Cone Square Sphere Cuboid Cylinder Parallelogram

Solution:

Cone Sphere Cuboid Cylinder

Example 2: State whether the following are true or false.

1. A three-dimensional shape has 3 dimensions.
2. Three-dimensional shapes are also called flat shapes.
3. Three-dimensional shapes occupy space.
4. All three-dimensional shapes have flat faces.

Solution:

1. True
2. False. Three-dimensional shapes are also called solid shapes.
3. True
4. False. Sphere is a three-dimensional shape with no flat face.

Example 3: Complete the table with attributes of the 3D shapes listed.

Solution:

Example 4: Match the object with its shape.

Solution:

1. – (iii)
2. – (i)
3. – (iv)
4. – (ii)

Example 5: Calculate the surface area of a cuboid with a width of 4 units, length of 3 units, and height of 5 units. 

Solution:

Given, the cuboid has three units of length, four units of width, and five units of height.

Surface area of the cuboid $= 2 \times (\text{lw} + \text{wh} + \text{lh})$ square units

$= 2 × (\text{lw} + \text{wh} + \text{lh})$

$= 2[(3 \times 4) + (4 \times 5) + (3 \times 5)]$

$= 2(12 + 20 + 15)$

$= 2(47)$

$= 94$ square units

Therefore, the surface area of the given cuboid is 94 square units.

Example 6: Jane likes to drink milk from a cylinder-shaped glass. Her glass has 15 units of height and 3 units of base radius. How much milk can she fill in the glass?

Solution:

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

Using the formula for the volume of a cylinder, we can find the volume of the glass.

The volume of the glass, $\text{V} = πr²\text{h}$

$= π(3)²​​​​​​(15)$

$= 135π$

$= 424.11 in³$

Therefore, Jane can fill approximately 424 cubic units of milk in her glass.