[Maths Class Notes] on What are Solid Shapes? Pdf for Exam

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.

 

 

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.

 

 

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

 

 

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

 

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

 

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

 

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

 

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

                                                                     

 

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

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:

1. Solid figures are basically three-dimensional objects, which means that they have length, height and width.  

2. Because solid figures have three dimensions, they have depth and take up space in our universe.  

3. Solid figures are identified according to the features that are unique to each type of solid.  

4. 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:

 

 

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.