1. Write all formulas of circles and give examples of each (means how you are applying the formula, you can one circle shape object and take measurements or else take examples from text book)
Answers
Answer:
pie r square
Step-by-step explanation:
pie r square
Answer:
The circle is a two-dimensional figure, which has its area and perimeter. The perimeter of the circle is also called the circumference, which is the distance around the circle. The area of the circle is the region bounded by it in a 2D plane. Let us discuss here circle definition, formulas, important terms with examples in detail.
Step-by-step explanation:
Circle Definition
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle. The circle formula in the plane is given as:
(x-h)2 + (y-k)2 = r2
where (x,y) are the coordinate points
(h,k) is the coordinate of the centre of a circle
and r is the radius of a circle.
How to Draw a Circle?
In maths projects for class 10 on circles, the construction of a circle, all the properties and terminologies are explained in detail. To understand what circles are in simple terms, go through circles for class 10, and also try the following exercise –
Circles
Take an empty sheet of paper and mark a single point on the sheet, somewhere in the middle of the sheet, and name it to point O.
Select a random length for radius, for example, 3 cm.
Using a ruler, keep the reference zero mark on point O and randomly mark 3 cm away from point O in all the direction.
Mark as many points as you want away from point O, but all of them should be exactly 3 cm away from point O.
If you’ve selected sufficient points, you may notice that the shape is starting to resemble a circle and this is exactly what the definition of a circle is.
Parts of Circle
A circle has different parts based on the positions and their properties. The different parts of a circle are explained below in detail.
Annulus-The region bounded by two concentric circles. It is basically a ring-shaped object. See the figure below.
Annulus
Arc – It is basically the connected curve of a circle.
Sector – A region bounded by two radii and an arc.
Segment- A region bounded by a chord and an arc lying between the chord’s endpoints. It is to be noted that segments do not contain the centre.
See the figure below explaining the arc, sector and segment of a circle.
Arc, sector and segment of a circle
Centre – It is the midpoint of a circle.
Chord- A line segment whose endpoints lie on the circle.
Diameter- A line segment having both the endpoints on the circle and is the largest chord of the circle.
Radius- A line segment connecting the centre of a circle to any point on the circle itself.
Secant- A straight line cutting the circle at two points. It is also called an extended chord.
Tangent- A coplanar straight line touching the circle at a single point.
See the figure below-representing the centre, chord, diameter, radius, secant and tangent of a circle.
Circles perimeter
Radius of Circle (r)
A line segment connecting the centre of a circle to any point on the circle itself “. The radius of the circle is denoted by “R” or “r”.
Radius of a Circle
Diameter (d) of Circle
A line segment having both the endpoints on the circle. It is twice the length of radius i.e. d = 2r. From the diameter, the radius of the circle formula is obtained as r= d/2.
Diameter of a Circle
Also, read:
Radius Of A Circle
Secant Of A Circle
Sector Of A Circle
Tangent Of A Circle
Concentric Circles
Equation Of A Circle
Circle Formulas
We know that a circle is a two-dimensional curve-shaped figure, and the two different parameters used to measure the circle are:
Area of circle
Circumference of a circle
Let us discuss here the general formulas for area and perimeter/circumference of a circle.
Area and Circumference of a Circle
Circumference (C) The circumference of a circle is defined as the
distance around the circle. The word ‘perimeter’
is also sometimes used, although this usually
refers to the distance around polygons, figures made up of the straight line segment.
A circle circumference formula is given by
C = πd = 2 π r
Where, π = 3.1415
Circumference of a Circle
Area (A) Area of a circle is the amount of space occupied by the circle.
The circle formula to find the area is given by
Area of a circle = πr2
Area of a Circle
Circle Area Proof
We know that Area is the space occupied by the circle.
Consider a concentric circle having an external circle radius to be ‘r.’
Area of a Circle Proof
Open all the concentric circles to form a right-angled triangle.
The outer circle would form a line having length 2πr forming the base.
The height would be ‘r’
Therefore the area of the right-angled triangle formed would be equal to the area of a circle.