We come across a number of objects of different shapes and sizes in our day to day life. There are golf balls, doormats, ice-cream cones, coke cans and so on. These objects have different characteristic properties such as length, breadth, diameter, etc. which set them apart from one another. But no matter how different their dimensions are, all of them occupy space and have three dimensions. So they are referred to as three-dimensional or solid shapes. In this article, we will discuss the various 3D shapes, surface area and volumes, and the process of making 3D shapes using nets with the help of 2D Shapes.
What are 3D Shapes?
In Geometry, 3D shapes are known as three-dimensional shapes or solids. 3D shapes have three different measures such as length, width, and height as its dimensions. The only difference between 2D shape and 3D shapes is that 3D shapes do not have a thickness or depth. Usually, 3D shapes are obtained from the rotation of the 2D shapes. The faces of the solid shapes are the 2D shapes. Some of the examples of the 3D shapes are a cube, cuboid, cone, cylinder, sphere, prism and so on.
Surface Area and Volume of 3D shapes
The two different measures used for measuring the 3D shapes are:
- Surface Area
Surface Area is defined as the total area of the surface of the two-dimensional object. The surface area is measured in terms of square units, and it is denoted as “SA”. The surface area can be classified into three different types. They are:
- Curved Surface Area (CSA) – Area of all the curved regions
- Lateral Surface Area (LSA) – Area of all the curved regions and all the flat surfaces excluding base areas
- Total Surface Area (TSA) – Area of all the surfaces including the base of a 3D object
Volume is defined as the total space occupied by the three-dimensional shape or solid. It is measured in terms of cubic units and it is denoted by “V”.
Properties of 3D shapes
The three important properties that differentiate the different 3D shapes are given below:
- Faces – A face is a curve or flat surface on the 3D shapes.
- Edges – An edge is a line segment between the faces.
- Vertices – A vertex is a point where the two edges meet.
3D Shapes using Nets
A net is a flattened out three-dimensional solid. It is the basic skeleton outline in two dimensions, which can be folded and glued together to obtain the 3D structure. Nets are used for making 3D shapes. Let us have a look at nets for different solids and its surface area and volume formula
A cuboid is also known as a rectangular prism. the faces of the cuboid are a rectangle in shape. All the angle measures are 90 degrees. It has
Faces – 6
Edges – 12
Vertices – 8
Take a matchbox. Cut along the edges and flatten out the box. This is the net for the cuboid. Now if you fold it back and glue it together in a similar fashion as you opened it, you get the cuboid.
Surface Area of a Cuboid, SA = 2(lb+bh+lh) Square units
Volume of a Cuboid, V = lbh Cubic units
A cube is defined as a three-dimensional square with 6 equal sides. All the faces of the cube have equal dimension. It has
Faces – 6
Edges – 12
Vertices – 8
Take a cheese cube box and cut it out along the edges to make the net for a cube.
Surface Area of a Cube, SA =6a2Square units
Volume of a Cube, V = a3 Cubic units
A cone is a solid object that has a circular base and has a single vertex. it is a geometrical shape that tapers smoothly from the circular flat base to a point called apex. It has
Faces – 2
Edges – 1
Vertices – 1
Take a birthday cap which is conical in shape. When you cut a slit along its slant surface, you get a net for cone.
Surface Area of a Cone, SA = πr(r +√(r2+h2) Square units
Volume of a Cone, V = ⅓ πr2h Cubic units
A cylinder is a solid geometrical figure, that has two parallel circular bases connected by a curved surface. It has
Faces – 3
Edges – 2
Vertices – 0
When you cut along the curved surface of any cylindrical jar, you get a net for cylinder. The net consists of two circles for the base and the top and a rectangle for the curved surface.
Surface Area of a Cylinder, SA = 2πr(h +r) Square units
Volume of a Cylinder, V = πr2 h Cubic units
A pyramid, also known as a polyhedron. A pyramid can be any polygon, such as a square, triangle and so on. It has three or more triangular faces that connect at a common point is called apex. For the square-based pyramid, it has
Faces – 5
Edges – 8
Vertices – 5
The net for a pyramid with a square base consists of a square with triangles along its four edges.
Surface Area of a pyramid, SA = B + L Square units
The volume of a pyramid, V = ⅓ Bh Cubic units
From the above discussion, students would be able to recognize the importance of shapes and forms to a great extent. However, to let what they have learned to sink in, students have to attempt practice questions with solved answers. Learn types of a prism and its examples online at BYJU’s.