3D Shapes

Geometry is one of the important branches of Mathematics that involves different shapes and sizes of different figures and their properties. Geometry can broadly be divided into two categories: \(2D\) geometry and \(3D\) geometry. \(2D\) geometry deals with flat shapes like lines, curves, polygons, etc., that can be drawn on a piece of paper. On the other hand, solid geometry includes objects of three-dimensional shapes such as cubes, cylinders, spheres, etc. The shapes that can be measured in three directions are called three-dimensional shapes. These shapes are also called solids. Here we will discuss a few fundamental features of 3D Shapes and three-dimensional geometry.

What Are 3D Shapes?

\(3D\) Shapes Definition: The shapes that can be measured in three dimensions are known as three-dimensional shapes. Solids are another name for these shapes. Three-dimensional shapes are measured by their length, width, and height (or depth or thickness. These shapes are also called solids.

What Are 3D Shapes Examples?

Our surroundings are full of three-dimensional shapes. These shapes are found around us in daily life, such as books, containers, gas cylinders, balls, ice cream cones, etc.

What Are the Properties of 3D Shapes?

The three coordinate axes, \(x\)-axis, \(y\)-axis, and \(z\)-axis define the shape of a three-dimensional shape. We can imagine every \(3D\) shape in the \(xyz\) plane. In general, we can classify the \(3D\) shapes based on the number of their faces, vertices, and edges.
Let us talk about the faces, vertices, edges.
Faces: Any of the individual flat surfaces of a solid object is known as the face of that object.
Vertex: In a \(3\)-dimensional object, a point where two or more lines meet is known as a vertex. Also, a corner can be referred to as a vertex.
Edge: An edge is a line segment joining two vertices.

Let us take some examples of \(3D\) shapes and discuss the faces, vertices, and edges.

Cuboid

A cuboid has \(6\) faces, \(8\) vertices, and \(12\) edges.

The total surface area (TSA) of a cuboid is the sum of the lateral surface area and top, bottom flat surface areas. If the length, breadth, and height are known we can easily find out the volume of the cuboid by the following formula: \(\left( {{\rm{volume}} = {\rm{length}} \times {\rm{breadth}} \times {\rm{height}}} \right).\)

Cube

The cube has \(6\) faces, \(8\) vertices, and \(12\) edges. The (TSA) total surface area of a cube is the sum of the six square faces. If one of the edges is known then the volume can be calculated \(\left( {{\rm{volume}} = {\rm{edge}} \times {\rm{edge}} \times {\rm{edge}}} \right).\)

Cylinder

A cylinder is a basic three-dimensional geometric object, with one curved surface and two circular surfaces at the ends. The cylinder has three faces, one curved face and two flat circular faces, two edges (where two faces meet) and it has no vertices (corners where two edges meet) as it has no corners.

So, it has three faces, zero vertices, and two edges(circular).
We can find the volume of the cylinder if we multiply the height of the cylinder and one of the circular base areas of it. 

Cone

A cone has two faces. One is flat and the other one is curved. One vertex and one edge. We can calculate the volume and surface area of a cone if its height and radius are known. The total surface area of the cone is the sum of the curved surface and the flat surface area. We can find the volume of it by finding one-third of the product of the circular base and the height of the cone.

Sphere

All the points on the surface of a sphere are equidistant from the centre. It has no vertex and no edges. It has only one curved surface. We can find out the surface area and the volume of the sphere if the radius of the sphere is known.

Triangular Prism

It has five faces, six vertices, nine edges.
The total surface area of a triangular prism is the sum of two flat triangular faces and three rectangular faces. We can find the volume of it by finding the product of the triangular base and the height of the prism.

Triangular Pyramid

It has four faces, four vertices, six edges.
The total surface area of a triangular pyramid is the sum of four triangular flat faces. We can find the volume of it by finding one-third of the product of the triangular base and the height of the pyramid.

What Do You Understand by the Nets of 3D Shapes?

The net of a three-dimensional shape is the outlines of its faces which, when joined together, forms the shape.
Let us discuss the nets of some \(3D\) shapes.

Net of a Cuboid

If we open a cuboidal box in a way that it lies in a plane surface (\(3D\) shape becomes \(2D\) shape), we will get the net of the cuboid. We will get six rectangular pieces in the net of a cuboid.
A cuboid can be drawn in \(54\) different nets of three different lengths. One of them is shown below:

Net of a Cube

There are \(11\) possible nets for a cube, as shown in the following figure.

After opening a cube in the same way, we will get six square faces (the area of the faces are the same).

Net of a Cylinder

A cylinder has three faces. If we separate its top and bottom faces, we will get two circular bases and if we open up its curved face, we will get a rectangle.

Net of a Cone

A cone has two faces. If we separate them we will get one circular face and a sector that is known as the curved face of the cone.

Net of a Triangular Prism

A triangular prism has three rectangular faces and two triangular faces. The net of it looks like,

Net of Square Pyramid

It has a square base and four triangular faces. The net of it looks like,

What are the Surface Area and the Volume of 3D Shapes?

Let us talk about the surface area and the volume of some \(3D\) shapes that we see very often, such as cuboid, cube, cylinder, cone, sphere, etc. Before discussing the surface area and the volume of the mentioned shapes in detail, we will know what exactly surface area and volume are.

Surface Area

The amount of outer space covering a three-dimensional shape is known as the surface area.
The area of any three-dimensional geometric shape can be classified into three types. These are:
1. Curved surface area
2. Lateral surface area
3. Total surface area

1. Curved Surface Area: The curved surface area is the area of all the curved regions of the solid.
2. Lateral Surface Area: The lateral surface area is the area of all the faces except the top and bottom faces or bases.
3. Total Surface Area: The total surface area is the area of all the faces (including top and bottom faces) of the solid object.

Volume

The volume of a three-dimensional solid is the amount of space it occupies or space enclosed by a boundary or occupied by an object or the capacity to hold something.

Solved Examples – 3D Shapes

Q.1. How many edges a cube has?
Ans: A cube has twelve equal edges.

Q.2. How many faces and edges a cylinder has?
Ans: A cylinder has three faces (one curved face, two flat circular faces) and two edges.

Q.3. How many vertices a sphere has?
Ans: In a \(3\) -dimensional object, a point where two or more lines meet is known as a vertex. Also, a corner can be referred to as a vertex.
There are no corners in a sphere. Therefore, a sphere has no vertices.

Q.4. How many edges a cone has?
Ans: A cone has only one edge.

Q.5. How many faces, vertices, and edges a triangular pyramid has?Ans: A triangular pyramid has four faces, four vertices, six edges.

Summary

In this article, we have learned about solid geometry that is known as \(3D\) geometry. 3D shapes, also called solids, will have length, width, and height (or depth or thickness) as the three measurements. There are different types of 3D shapes around us, such as cube, cuboid, cylinder, cone, sphere, triangular pyramid, square pyramid, triangular prism, etc. The above article discusses various three-dimensional shapes and their examples, their properties, and how to find their volume and surface area.

Frequently Asked Questions

The most commonly asked questions about 3D shapes are answered below:

Q.1. How many sides do 3D shapes have?
Ans: The number of sides depends on the 3D shapes. For example, a cube and a cuboid, both have twelve sides; on the other hand, a cylinder has two edges or sides.

Q.2. How do you figure out 3D shapes?
Ans: These shapes, also called solids, will have length, width, and height (or depth or thickness) as the three measurements.

Q.3. What do you call a 3D triangle?
Ans: We call a 3D triangle a triangular pyramid.

Q.4. What are 3D shapes with examples?
Ans: Shapes that can be measured in 3 directions are called three-dimensional shapes. Example: cube, cuboid, cylinder, cone, etc.
Q.5. What are the types of 3D shapes?
Ans: There are different types of 3D shapes around us, such as cube, cuboid, cylinder, cone, sphere, triangular pyramid, square pyramid, triangular prism, etc.