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Solid Shapes
Solid shapes are nothing but solids that consist of 3 dimensions, namely length, breadth, and height. Solid shapes are also known as 3D shapes. These solid shapes occupy space and are found in our daytoday life. We touch, feel, and use them. In this fun lesson, you can check out some interactive examples to know more and try your hand at solving a few interesting practice questions at the end of the page.
1.  What are Solid Shapes? 
2.  Solid Shapes and their Properties 
3.  Faces, Edges, and Vertices of Solid Shapes 
4.  FAQs on Solid Shapes 
What are Solid Shapes?
In mathematics, we study shapes and their different types and try to apply them in real life. We will now learn about each solid shape in detail. Solid shapes are classified into several categories. Some of them have curved surfaces; some are in the shape of pyramids or prisms.
Solid Shapes Definition: Solid shapes are threedimensional shapes that have length, breadth, and height as the three dimensions.
Let us first learn about solid shapes with curved surfaces with examples.
Solid Shapes and their Properties
Solid shapes correspond to threedimensional objects. Look around! Every other threedimensional object, be it a laptop, cellphone, an icecream cone, balls, etc, are examples of solid shapes. These occupy some space, have length, width as well as height. Let's explore types of solid shapes
 Sphere
 Cylinder
 Cone
 Pyramid
 Prism
Sphere
A sphere is a solid shape, absolutely round in shape, defined in threedimensional space. Every point on the surface is equidistant from the center.
The table below shows the properties of a sphere:
Properties  Surface Area  Volume 


4πr^{2}  (4/3)πr^{3} 
Cylinder
A cylinder is a solid shape defined on a threedimensional plane. It holds two parallel bases, circular in shape, joined by a curved surface(like a tube), at a fixed distance.
The table below shows the properties of a cylinder:
Properties  Surface Area  Volume 


2πr (r+h)  πr^{2 }h 
Cone
A cone is a distinctive solid shape defined in a threedimensional space. It has a flat surface and a curved surface, pointing towards the top. It is formed by a set of line segments connected from the circular base to a common point, known as the apex or vertex. Based on how the apex is aligned to the center of the base, a right cone or an oblique cone is formed.
The table below shows the properties of a cone where r denotes radius, h represents height and s represents slant height of the cone:
Properties  Surface Area  Volume 


π r(r + s)  1/3 πr^{2 }h 
Pyramid
A pyramid is a solid shape or a polyhedron with a polygon base and all lateral faces are triangles. Pyramids are typically described by the shape of their bases. A pyramid with a:
 Triangular base is called aTetrahedron.
 A quadrilateral base is called a square pyramid.
 Pentagon base is called a pentagonal pyramid.
 Regular hexagon base is called a hexagonal pyramid.
The table below shows the properties of a pyramid: (BA = base area, P = perimeter, A = altitude, and SH = slant height )
Properties  Surface Area  Volume 


BA + 1/2 × P × (SH) 
1/3 BA^{2} 
Prisms
A prism is a solid shape defined on a 3dimensional plane with two identical shapes facing each other. The different types of prisms are triangular prisms, square prisms, pentagonal prisms, hexagonal prisms, etc. Prisms are also broadly classified into regular prisms and oblique prisms.
The table below shows the properties of a prism: (BA = base area, P = perimeter, H = height)
Properties  Surface Area  Volume 


2 × (BA) + P × H  BA × H 
Polyhedrons/Platonic Solids
Platonic solids have identical faces to regular polygons. There are five polyhedrons.
 Tetrahedron with four equilateraltriangular faces
 Octahedron with eight equilateraltriangular faces
 Dodecahedron with twelve pentagon faces
 Icosahedron with twenty equilateraltriangular faces
 Hexahedron or cube with six square faces.
The table below shows the properties of platonic shapes: (EL = edge length)
Properties of Cube  Surface Area  Volume 


6 × (EL)^{2}  (EL)^{3} 
Faces, Edges, and Vertices of Solid Shapes
As mentioned before, solid shapes and objects are different from 2D shapes and objects because of the presence of the three dimensions  length, breadth, and height. As a result of these three dimensions, these objects have faces, edges, and vertices. Let's understand these three in detail.
Faces of Solid Shapes
 A face refers to any single flat surface of a solid object.
 Solid shapes can have more than one face.
Edges of Solid Shapes
 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 of Solid Shapes
 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.
For example:
Solid Shapes  Faces  Edges  Vertices 

Sphere 
1 
0  0 
Cylinder 
2 
2  0 
Cone 
1 
1  1 
Cube 
6 
12  8 
Rectangular Prism 
6 
12  8 
5  9  6  
7  15  10  
8  18  12  
5  8  5  
4 
6  6  
6  10  6  
7  12  7 
Tips and Tricks
 Rhyme to remember solid shapes:
"Solid shapes are fat, not flat.
Find a cone in a birthday hat!
You see a sphere in a basketball,
And a cuboid in a building so tall!
You see a cube in the dice you roll,
And a cylinder in a shiny flag pole!"
 Moving your fingers along geometric shapes will help you understand the concept of faces, edges, and vertices.
Important Points
 Solids or threedimensional objects have 3 dimensions, namely length, breadth, and height.
 Solid shapes have faces, edges, and vertices.
 Learning about solid shapes will help us in our daytoday life as most of our activities revolve around and depend on them.
Related Topics
Solid Shapes Examples

Example 1: A construction worker wants to build a solid sphere using cement. He wants to know the amount of cement required to construct a sphere of radius 10 inches. Find the volume of the sphere using the given radius.
Solution:
The radius of the sphere (r) = 10 inches. We know the formula for the volume of a sphere: v = 4/3 π r^{3}. Substituting the value of the radius in the above formula, we get: v= 4/3 π r^{3 }= 4/3 π (10)^{3 }= 4188.8 inches^{3}. Therefore, the volume of the cemented sphere is 4188.8 inches^{3}

Example 2: Identify the regular polyhedron from the images shown below.
Solution:
Regular polyhedrons include:
Prisms
Pyramids
Platonic solidsThe given examples of polyhedrons must come under these categories. Thus, the Egyptian pyramids and Rubik's cubes are polyhedrons.

Example 3: Find the area of the squareshaped floor room which is made up of 100 square tiles of side 15 inches.
Solution:
Area of one tile = 15 inch × 15 inch= 225 square inches. We know that there are 100 tiles on the floor of the room. Thus, the area occupied by 100 tiles is the floor area = 100 × 225 square inches = 22500 square inches. Therefore, the area of the floor is 22500 square inches.
FAQs on Solid Shapes
What is a Solid Shape?
The objects that are threedimensional with length, breadth, and height defined are known as solid shapes.
What can a Solid Shape Also be Called?
In geometry, a solid shape can also be called a threedimensional shape.
How Many Solid Shapes are There?
The list of solid shapes includes cube, cuboid, sphere, cone, hemisphere, prism, cylinder, pyramid, etc.
What is the Volume of a Solid Shape?
The volume of solid shapes refers to the amount of cubic space filled within the shapes. To find the volume, we need the measurements of the three dimensions.
Is a Sphere Solid or Flat Shape?
A sphere is a solid shape with no edges or vertices (corners).
What are the Properties of Solid Shapes?
Solid shapes are threedimensional objects. They have three dimensions  length, width, and height. Being threedimensional, they take up space in the universe. Solid shapes are identified according to the features edges, vertices, faces, etc.
What are the Flat and Solid Shapes?
Flat shapes are also known as plane shapes which are 2D shapes consisting of straight lines, curved lines, or both. Whereas solid shapes are 3D shapes consisting of length, breadth, and height. The difference between flat and solid shapes is the dimensions. For example, a square is a flat shape and its counter solid shape is a cube which is a 3D shape.
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