# Circle Cube Cuboid

Feb 11, 2023

We have to learn Rhombus, Parallelogram, Trapezium in the previous post. We will learn here Circle, Cube and Cuboid in details. Play with circle as a fun game. Circle Cube Cuboid

You are familiar with this figure. This is a circle. It is a closed figure. Violet colored figure is also a circle. In which, a point ‘P’ is allocated in the center of circle. It is called Centre of Circle. Now you have to familiar with the center of circle.

Here, we can draw a fixed line segment from the point and move around the given point with equal line segment to make a closed figure with a boundary just like a circle. Hence, the equal line segment touches the boundary at every points. This equal line segment is called the Radius. It is denoted by ‘r’. Now you have to familiar with the radius. Circle Cube Cuboid

Now, we learn the diameter of circle. The diameter is the double in the length of radius (d = 2r). It is denoted by ‘d’. We just draw a line segment to cross the center of circle from a point on the boundary and end at another point on the boundary. The line segment is called the Diameter.

##### Definition of Circle:

A circle is a closed two dimensional  plane figure in which a point is allocated in the center called the center of circle. To set of all the points on the boundary is at the equidistant from the center of circle. Every line pass through the center of circle forms the line of symmetry. Also, it has rotational symmetry around the center of circle for every angles.

A circle is the locus of the points at drawn at an equidistant from the center of circle. The distance from the center of the circle to the its outer boundary is known as its radius. The diameter is a line segment which pass through the center of circle and end at two different points on the boundary. The diameter is equal to twice of the radius. Circle Cube Cuboid

##### Perimeter or Circumference of Circle:

You are familiar with the perimeter term. It is the total length of outer boundary of a closed two dimensional plane figure. Here, Circumference is another termed used for the perimeter of circle. Also, we can say that the Circumference is the total length of outer boundary of a closed two dimensional plane figure. Circle Cube Cuboid

Circumference of Circle:

= 2 x π x r

= π x (2 r)

= π x d

Note: The value of π (Pie) is the ratio of the circumference and diameter of circle. It is approximately equal to 3.14.

Π = Circumference/Diameter

It is the 16th letter of the Greek alphabet and used for mathematical constant. Π is a irrational number. But in fraction, π = 22/7 is a rational number. Here, we can use both π or 22/7. If you want to find the value, you can use 22/7. Otherwise remains it in the form of π.

##### Area of Circle:

We are familiar with the term of area. Area of the circle is the space occupied inside the circumference of circle. As shown in above figure, Blue colored space in the circle is the area of circle. Circle Cube Cuboid

Area of Circle:

= πr2

##### Some important terms:

Sector of Circle:

As shown in above figure, the sector in the circle is pink colored space between drawn two radius from the center of circle with an angle at the center of circle.

As shown in another circle, Smaller sector of circle is Minor sector and Larger sector of circle is Major circle.

##### Chord of Circle:

As shown in above figure, the chord of circle is red colored line drawn between two points on the circumference ether pass through the center of circle or not. The diameter is the largest chord of a circle.

Segment of Circle:

As shown in above figure, the segment in the circle is yellow colored space between drawn chord and circumference.

In another circle, the smaller part of yellow colored space is called Minor segment and the larger part of yellow colored space is called Major segment.

##### Properties of Circle:

#  It has a fixed point in the circle called center of circle.

# A line segment drawn from the circumference to the center of circle called radius of circle.

# A line segment drawn between circumference pass through the center of circle called diameter of circle.

# The diameter of circle divides the circle into two equal parts.

# The diameter is equal to the double of the radius.

# The largest chord in the circle is the diameter.

# The circumference = 2πr

# Area = πr2

# Some important termed as Sector, Chord, Segment etc.

##### What is Cube?

I know very well that you are familiar with this figure to see around of us. This is a cube. A cube is a solid three dimensional figure. It has the volume, surface area. The volume is measured in cm3, m3, litre etc. The area is measured in cm2, m2 etc. The cube has edge, vertex and face. As shown in figure below. It is also called regular hexahedron. Circle Cube Cuboid

It has 6 square faces. 6 square plane figures attached with each other like above figure gives you a cube.

It has 12 edges. Each edges are equal in length. All these edges are line segment connect with each other.

It has 8 vertices. Each vertex is the intersecting point of three edge of the cube. Vertex is also a point in the cube.

In a cube, Everywhere is a right angles. Each edges, faces are perpendicularly connected with each other.

It is a solid three dimensional figure and have equal length, width and height. Length is denoted by ‘l’ and Width is denoted by ‘b’ and Height is denoted by ‘h’.

##### Surface Area of Cube:

We know very well. It has 6 faces just like a square. There are four lateral surface and two are the top and the bottom surface. We have to learn in the previous post. How to find the area of a square.

##### How to find the area of later surface?

There are four lateral squared surfaces. The sum of all the four squared lateral surface is called the lateral surface area of a cube. All the edges are equal in length ‘l’. L = B = H = ‘l’.

The lateral surface area of a cube:

= (l)2 +(l)2 + (l)2 + (l)2

= 4 (l)2

The top and the bottom squared surface area:

= (l)2 +(l)2

= 2(l)2

The surface area of a cube:

= 4 (l)2 + 2 (l)2

= 6 (l)2

##### Volume of Cube:

It has the capacity to stored the liquid like milk, oil etc. The capacity of a utensil is to stored called the volume. Here, cube has equal length, width and height. If water is kept in an object is calculate by its volume. Let a cube of length of edge is ‘a’. l = b = h = ‘a’.

The volume of a cube:

= l x b x h

= (a)3 m3.

Note: 1 cm3 = 1 ml; 10 cm3 = 1000 ml = 1 litre; 1 m3 = 1000,000 ml = 1000 litre.

##### Properties of Cube:

# It has 6 faces, 8 vertices and 12 edges.

# It has 6 squared faces with equal dimension.

# The plane angle of a cube are right angle.

# The Diagonal of the face = √2 a

# The Diagonal of Cube = √3 a

# The lateral surface area of cube = 4 a2

# The surface area of cube  = 6 a2

# The volume of cube = a3

##### What is cuboid?

I know very well that you are familiar with this figure to see around of us. This is a cuboid. A cuboid is a solid three dimensional figure. It has the volume, surface area. The volume is measured in cm3, m3, litre etc. The area is measured in cm2, m2 etc. The cuboid has edge, vertex and face. As shown in figure below. The figure is also known as rectangular hexahedron, rectangular cuboid, right rectangular prism, rectangular box, rectangular parallelepiped, right cuboid.

It has 6 faces. The opposite faces are equal in area. All the faces attached with each other like above figure gives you a cuboid.

It has 12 edges. The opposite edges are equal in length. All these edges are line segment connect with each other.

It has 8 vertices. Each vertex is the intersecting point of three edge of the cuboid. Vertex is also a point in the cuboid.

In a cuboid, Everywhere is a right angles. Each edges, faces are perpendicularly connected with each other.

It is a solid three dimensional figure and have length, width and height. Length is denoted by ‘l’ and Width is denoted by ‘b’ and Height is denoted by ‘h’.

##### Surface Area of Cuboid:

We know very well. It has 6 faces. There are four lateral surface and two are the top and the bottom surface. We have to learn in the previous post. How to find the area of a rectangle.

##### How to find the area of later surface?

There are four lateral  surfaces. The sum of all the four lateral surface is called the lateral surface area of a cuboid. There are three measure in the cuboid. The length is denoted by ‘l’. The width is denoted by ‘b’. The height is denoted by ‘h’.

The lateral surface area of a cuboid:

= (l x h) +(l x h) + (b x h) + (b x h)

= 2 (l x h) + 2 (b x h)

= 2 (l x h + b x h)

= 2 (l + b) x h

The top and the bottom squared surface area:

= (l x b) +(l x b)

= 2 (l x b)

The surface area of a cuboid:

= 2 (l + b) x h + 2 (l x b)

= 2 lh + 2 bh + 2 lb

= 2 (lh + bh + lb)

##### Volume of Cuboid:

It has the capacity to stored the liquid like milk, oil etc. The capacity of a utensil is to stored called the volume. Here, cuboid has length, width and height. If water is kept in an object is calculate by its volume. Let a cuboid of length, width and height are l, b and h.

The volume of a cuboid:

= l x b x h

= lbh m3.

Note: 1 cm3 = 1 ml; 10 cm3 = 1000 ml = 1 litre; 1 m3 = 1000,000 ml = 1000 litre.

##### Properties of Cuboid:

# It has 6 faces, 8 vertices and 12 edges.

# It has 6 faces with opposite equal dimension.

# The plane angle of a cuboid are right angle.

# The Diagonal of the face = √(l2 + b2) or √(h2 + b2) or √(l2 + h2)

# The Diagonal of Cuboid = √(l2 + b2 + h2)

# The lateral surface area of cuboid = 2 (l + b) x h

# The surface area of cuboid  = 2 (lh + bh + lb)

# The volume of cuboid = lbh.

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