 # Three Dimensional Shapes

Geometry is one of the practical sections of Mathematics which involves various shapes and sizes of different figures and their properties. Geometry can be divided into two types: plane and solid geometry. Plane 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 involves objects of three-dimensional shapes such as cylinders, cubes, spheres, etc. Here we will discuss a few fundamental elements of solid geometry or the three-dimensional geometry.

## What are Three-Dimensional Shapes?

Shapes which can be measured in 3 directions are called three-dimensional shapes. These shapes are also called solids. Length, width, and height (or depth or thickness) are the three measurements of the three-dimensional shapes. These are the part of three-dimensional geometry. They are different from 2D shapes because they have thickness. Several examples can be found in everyday life. Some of them are: ## Solid Shapes in Maths

The three-dimensional objects having depth, width and height are called solid shapes. Let us consider a few shapes to learn about them. You can find many examples of solid shapes around you, such as mobile, notebook or almost everything you can see around is a solid shape.

Also Check: 2D Shapes ## Surface Area and Volume of 3D shapes

The two distinct measures used for defining the 3D shapes are:

• Surface Area
• Volume

Surface Area is defined as the total area of the surface of the three-dimensional object.  It is denoted as “SA”. The surface area is measured in terms of square units. The three different classifications of surface area are defined below. They are:

• Curved Surface Area (CSA) is the area of all the curved regions
• Lateral Surface Area (LSA) is the area of all the curved regions and all the flat surfaces excluding base areas
• Total Surface Area (TSA) is the 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 object. The volume is denoted as “V”. It is measured in terms of cubic units.

## Faces, Edges, and Vertices of 3D Shapes

Three-dimensional shapes have many attributes, such as vertices, faces, and edges. The flat surfaces of the 3D shapes are called the faces. The line segment where two faces meet is called an edge. A vertex is a point where three edges meet. Faces, Edges and Vertices

### How to Make 3d Shapes for Maths Project

If you know what three-dimensional shapes are, it would be easy for you to build a 3d shape project for a house or a building. This would be easy for the students to make as they can measure the rooms easily. Rest all they need is cardboard, glue, scissors and art supplies to make it look exactly like a mini house or building. Here, we are going to discuss the list of different three-dimensional shapes with its properties and the formulas of different 3D shapes

### Cube A cube is a solid or three-dimensional shape which has 6 square faces. The cube has the following properties.

• All edges are equal
• 8 vertices
• 12 edges
• 6 faces

The surface area and the volume of the cube are given below:

The Surface Area of a Cube = 6asquare units

The volume of a Cube = a cubic units

### Cuboid A cuboid also called a rectangular prism, where the faces of the cuboid are a rectangle in shape. All the angle measures  90 degrees. The cuboid has

• 8 vertices
• 12 edges
• 6 faces

The surface area and the volume of the cuboid are given below:

The Surface Area of a Cuboid = 2(lb+bh+lh) Square units

The volume of a Cuboid = lbh Cubic units

### Prism A prism is a 3D shape which consists of two equal ends, flat surfaces or faces, and also have identical cross-section across its length. Since the cross-section looks like a triangle, the prism is generally called a triangular prism. The prism does not have any curve. Also, a prism has

• 6 vertices
• 9 edges
• 5 faces – 2 triangles and 3 rectangles

The surface area and the volume of the prism are given below:

The Surface Area of a Prism =2(Base Area)+ (Base perimeter × length) square units

The volume of a Prism =  Base Area × Height Cubic units

### Pyramid A pyramid a solid shape, whose outer faces are triangular and meet to a single point on the top. The pyramid base can be of any shape such as triangular, square, quadrilateral or in the shape of any polygon. The most commonly used type of a pyramid is the square pyramid, i.e., it has a square base and four triangular faces. Consider a square pyramid, it has

• 5 vertices
• 8 edges
• 5 faces

The surface area and the volume of the pyramid are given below:

The Surface Area of a Pyramid = (Base area) + (1/2) × (Perimeter) × (Slant height) Square units

The volume of a Pyramid =  1/ 3 × (Base Area) × height Cubic units

### Cylinder A cylinder is defined as the three-dimensional geometrical figure which has two circular bases connected by a curved surface. A cylinder has

• No vertex
• 2 edges
• 2 flat faces – circles
• 1 curved face

The surface area and the volume of the cylinder are given below:

The Surface Area of a Cylinder = 2πr(h +r) Square units
The curved surface area of a cylinder = 2πrh

The volume of a Cylinder =  πr2 h Cubic units

### Cone A cone is a three-dimensional object or solid, which has a circular base and has a single vertex. The cone is a geometrical figure that decreases smoothly from the circular flat base to the top point called the apex. A cone has

• 1 vertex
• 1 edge
• 1 flat face – circle
• 1 curved face

The surface area and the volume of the cone are given below:

The Surface Area of a Cone = πr(r +√(r2+h2) Square units
The curved surface area of a cone =πrl square units
Slant height of a cone = l = √(r2+h2) units

The volume of a Cone = ⅓ πr2h Cubic units

### Sphere A sphere is a three-dimensional solid figure which is perfectly round in shapes and every point on its surface is equidistant from the point is called the centre. The fixed distance from the centre of the sphere is called a radius of the sphere. A sphere has

• No vertex
• No edges
• 1 curved face

The surface area and the volume of the sphere are given below:

The Curved Surface Area of a Sphere = 2πr² Square units

The Total Surface Area of a Sphere = 4πr² Square units

The volume of a Sphere = 4/3(πr3) cubic units