Key Properties and Examples of Solid Shapes
You’re reading this on a laptop/computer; what is its shape? Cuboidal! That’s right! What is a Cuboid? It’s a solid shape. You see the ball you play with; what is its shape? Sphere! That’s right! What is a sphere? It’s a solid shape. Similarly is a cylinder, cones, etc. These are all different Solid Shapes. Let us know what solid shapes are in detail.
What is a Plane Figure?
Shapes are generally either two-dimensional shapes or flat plane geometry shapes. The sides can be made of straight or curved lines; the plane figures can have any number of sides. Plane figures made of lines are known as polygons. Squares and triangles are examples of polygons. Example: We can say figures drawn on paper that have only breadth and length are known as 2-d figures.
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What are Solid Shapes?
Many objects that you see in your day to day life, for example, books, pencil boxes, ice cream cones, footballs and cylinders, are all different solid shapes. All these objects in space occupy some shape and have three dimensions- breadth, length and height or depth.
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Solid Shapes Definition:
Solid shapes are three-dimensional objects. What this means is that all different solid shapes have a width, a height and a depth. For example, look at your computer, laptop, phone. Notice that it has a depth, a width and a height too.
This may make you think that different solid shapes are probably quite common in the environment around us, and you are right! Any shape with the three dimensions (width, depth, and height) is known to be a solid figure, and because we live in a three-dimensional world, we can find these solid figures all around us. In mathematics, there are many solid figures.
Let's look at these figures and some examples of them in our everyday life.
Rectangular Prisms and Cubes
A rectangular prism is a solid figure that has six sides, called faces, that are rectangles. This can be thought of as a fancy name for something that has the shape of a cardboard box. Rectangular prisms show up all around us. Some examples can be a book, a piece of furniture, or a jewelry box. A prism has
6 vertices
9 edges
5 faces – 2 triangles and 3 rectangles
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Types of Prisms
Cubes can be defined as a special case of rectangular prisms. Cubes are solid figures that have six faces which are all squares of the same exact size. A cube has six faces that are all rectangles, so a cube can be known as a rectangular prism.
The Cube has the Following Properties:
All edges are equal
8 vertices
12 edges
6 faces
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Cones and Pyramids
A cone is a solid figure that has a circular face on one end, called the base, and a point at the other end where the sides meet. I'm pretty sure we have all enjoyed an ice cream cone at one point in our lives. The cone that you put the ice cream in is an example of a cone, and what a delicious example! Some other examples could include a megaphone, a tee-pee tent, or a birthday party hat. We see that a parking cone is another example of a cone. A cone has
1 vertex
1 edge
1 flat face – circle
1 curved face
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A pyramid is a solid figure that has a polygon as its base on one end and triangular faces all meeting at a single point on the other end. Many of us have heard of the Great Pyramids of Egypt. These are perfect examples of a pyramid in the world around us. Some other examples of pyramids in the world around us are rooftops, certain buildings, and figurines. A square pyramid has
5 vertices
8 edges
5 faces
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Spheres and Cylinders
A sphere is known to be a solid figure which is round and it basically has the shape of a ball. For example, basketball is also a sphere. Another example of a sphere can be the earth we are standing on! When we look at a globe, we can see that the earth is three-dimensional and the Earth has the shape of a ball. Therefore, we can say that the earth is a sphere. A sphere has the following :
No vertex
No edges
1 curved face
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A cylinder is known to be a solid figure that has two circular bases and one curved side. A cylinder is similar to a cone, except that rather than only one circular base and a point on the other end, there are circular bases on both ends connected by the curved side. Some examples of cylinders are tubes, tree stumps, poles, and cans. A cylinder has the following properties:
No vertex
2 edges
2 flat faces – circles
1 curved face
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What is an Edge, Vertex, and a Face?
A vertex in a geometrical figure can be defined as a corner.
A line segment between faces is known as an edge.
A single flat surface is known as a face.
Cuboid
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A cuboid is a three dimensional solid. It has 6 faces (rectangular), 8 vertices and 12 edges. A cuboid has three dimensions such as length, width and height.
There are a few shapes that appear like cuboid shape are rectangular cuboid, rectangular box, right rectangular prism, right cuboid, rectangular parallelepiped,
Properties of Solid Shapes:
Solid figures are basically three-dimensional objects, which means that they have length, height and width.
Because solid figures have three dimensions, they have depth and take up space in our universe.
Solid figures are identified according to the features that are unique to each type of solid.
Specifically, you can observe the numbers of faces, edges, and vertices, as well as the shape of the base.
Questions to be Solved:
1: Find the number of faces, edges and vertices in the figure given below:
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Solution: The figure given above is a cylinder. And we already know that a cylinder has 0 vertices, 2 faces, and 0 edges.
2: The given problem is about Arthur and his greorganisationtion. Arthur needs to figure out the characteristics of the two gifts. He also wants to characterize the big round helium balloons. Arthur considers the first present, a large blue one. First, it has 6 faces. Next, they are all square, including the base. Then, the gift has 8 vertices and 12 edges. What is a gift?
Solution: The answer is that the large blue present is a cube.
FAQs on What Are Solid Shapes in Maths?
1. What is a solid shape in mathematics?
In mathematics, a solid shape is a three-dimensional (3D) object, which means it has length, width, and height. Unlike flat shapes, which are two-dimensional, solid shapes occupy space. They are also known as geometric solids or 3D shapes.
2. What is the difference between two-dimensional (2D) and three-dimensional (3D) shapes?
The main difference lies in their dimensions and the space they occupy. Here’s a simple breakdown:
Two-dimensional (2D) shapes are flat and have only two dimensions: length and width. Examples include squares, circles, and triangles. They can be drawn on a piece of paper but have no thickness.
Three-dimensional (3D) shapes, or solid shapes, have three dimensions: length, width, and height (or depth). They occupy volume. Examples include cubes, spheres, and cylinders.
3. What are the most common types of solid shapes?
Some of the most common solid shapes studied in the school curriculum include:
Cube: A shape with six identical square faces.
Cuboid: A shape with six rectangular faces (also called a rectangular prism).
Cylinder: A shape with two circular bases and one curved surface.
Cone: A shape with a circular base and a single vertex (point).
Sphere: A perfectly round shape with every point on its surface equidistant from its centre.
Pyramid: A shape with a polygon base and triangular faces that meet at a common vertex.
4. Can you provide some real-world examples of solid shapes?
Yes, solid shapes are all around us. For example:
A Rubik's Cube or a sugar cube is an example of a cube.
A book, a brick, or a duster is an example of a cuboid.
A birthday party hat or an ice cream cone is an example of a cone.
A can of soup or a battery is an example of a cylinder.
A football or a globe is an example of a sphere.
5. What are the faces, edges, and vertices of a solid shape?
Faces, edges, and vertices are the fundamental properties that describe many solid shapes:
Faces: These are the flat surfaces of a solid shape. For example, a cube has 6 faces.
Edges: These are the straight lines where two faces meet. A cube has 12 edges.
Vertices: These are the corners where three or more edges meet. A cube has 8 vertices. (The singular form is vertex).
6. How do the properties of a cube differ from those of a cuboid?
While a cube and a cuboid are very similar, there is one key difference in their properties. Both have 6 faces, 12 edges, and 8 vertices. However, the defining difference is the shape of their faces:
In a cube, all six faces are identical squares.
In a cuboid, the faces are rectangles, and only the opposite faces are identical.
Therefore, a cube is a special type of cuboid where all edges are of equal length.
7. Why is a sphere considered a solid shape if it has no flat faces, edges, or vertices?
A sphere is considered a solid shape because it fits the primary definition: it is a three-dimensional object that occupies space. While it lacks the flat faces, straight edges, and vertices seen in polyhedrons like cubes, it possesses volume and has a surface. Its entire surface is a single, continuous curved face. The classification of a solid shape depends on its dimensionality, not on having flat surfaces.
8. What is the purpose of a 'net' in understanding solid shapes?
A 'net' is a two-dimensional pattern of a solid shape that can be cut out and folded to form the three-dimensional model. The primary purpose of a net is to help visualise how a 3D shape is constructed from a flat surface. It is extremely useful in understanding the relationship between 2D and 3D geometry and is a crucial tool for calculating the surface area of a solid shape, as it displays all the faces in one flat layout.
