Article on area related to circles.
Answers
Answer:
Area of a circle is πr2, where π=22/7 or ≈3.14 (can be used interchangeably for problem-solving purposes)and r is the radius of the circle. π is the ratio of the circumference of a circle to its diameter.
Answer:
Area of a Circle
Area of a circle is πr2, where π=22/7 or ≈3.14 (can be used interchangeably for problem-solving purposes)and r is the radius of the circle.
π is the ratio of the circumference of a circle to its diameter.
Circumference of a Circle
The perimeter of a circle is the distance covered by going around its boundary once. The perimeter of a circle has a special name: Circumference, which is π times the diameter which is given by the formula 2πr
Segment of a Circle
A circular segment is a region of a circle which is “cut off” from the rest of the circle by a secant or a chord.
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Sector of a Circle
A circle sector/ sector of a circle is defined as the region of a circle enclosed by an arc and two radii. The smaller area is called the minor sector and the larger area is called the major sector.
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Angle of a Sector
The angle of a sector is that angle which is enclosed between the two radii of the sector.
Length of an arc of a sector
The length of the arc of a sector can be found by using the expression for the circumference of a circle and the angle of the sector, using the following formula:
L= (θ/360°)×2πr
Where θ is the angle of sector and r is the radius of the circle.
Area of a Sector of a Circle
Area of a sector is given by
(θ/360°)×πr2
where ∠θ is the angle of this sector(minor sector in the following case) and r is its radius
Area related to circles class 10 -1
Area of a sector
Area of a Triangle
The Area of a triangle is,
Area=(1/2)×base×height
If the triangle is an equilateral then
Area=(√3/4)×a2 where “a” is the side length of the triangle.
Area of segment APB (highlighted in yellow)
= (Area of sector OAPB) – (Area of triangle AOB)
=[(∅/360°)×πr2] – [(1/2)×AB×OM]
[To find the area of triangle AOB, use trigonometric ratios to find OM (height) and AB (base)]
Also, Area of segment APB can be calculated directly if the angle of the sector is known using the following formula.
=[(θ/360°)×πr2] – [r2×sin θ/2 × cosθ/2]
Where θ is the angle of the sector and r is the radius of the circle
Visualizations
Areas of different plane figures
– Area of a square (side l) =l2
– Area of a rectangle =l×b, where l and b are the length and breadth of the rectangle
– Area of a parallelogram =b×h, where “b” is the base and “h” is the perpendicular height.
Area related to circles class 10 -3
parallelogram
Area of a trapezium =[(a+b)×h]/2,
where
a & b are the length of the parallel sides
h is the trapezium height
Area of a rhombus =pq/2, where p & q are the diagonals.
Areas of Combination of Plane figures
For example: Find the area of the shaded part in the following figure: Given the ABCD is a square of side 28 cm and has four equal circles enclosed within.
Area related to circles class 10 -4
Area of the shaded region
Looking at the figure we can visualize that the required shaded area = A(square ABCD) − 4 ×A(Circle).
Also, the diameter of each circle is 14 cm.
=(l2)−4×(πr2)
=(282)−[4×(π×49)]
=784−[4×22/7×49]
=784−616
=168cm2