Formulas of Area and Perimeter of a Circle and Semi-Circle
AREA:
The Area of a Circle can be found either by its radius or diameter.
Radius of a circle is half of its diameter. That is,
radius = `frac{diameter}{2}`
Or we can say, diameter of a circle is double of its radius. That is,
diameter = 2 (radius)
In terms of radius, formula of Area of a Circle = π r²
where r is the radius of a circle.
Semi-circle is half of a circle.
So, half of area of a circle is an area of semi-circle.
Thus,
In terms of radius, Area of Semi-Circle = `frac{pi r^2}{2}`
In terms of diameter, formula of Area of a Circle =`frac{pi d^2}{4}`
where d is the diameter of a circle.
In terms of diameter, Area of Semi-Circle = `frac{pi d^2}{8}`
PERIMETER:
Perimeter of a Circle is also named as Circumference of a Circle.
The Perimeter of a Circle can also be found either by its radius or diameter.
In terms of radius, formula of Perimeter of a Circle = 2πr
where r is the radius of a circle.
Perimeter of a Semi-Circle consists of two parts: Half circle and a straight line.
Length of half circle = `frac{2pi r}{2}` = πr
Length of straight line = 2r
So,
In terms of radius, Perimeter of a Semi-Circle
= πr + 2r
= r (π + 2)
In terms of diameter, formula of Perimeter of a Circle = πd
where d is the diameter of a circle.
In semi-circle,
Length of half circle = `frac{pi d}{2}`
Length of straight line = d
So,
In terms of diameter, Perimeter of a Semi-Circle
= `frac{pi d}{2}` + d
= d (`frac{pi}{2}` + 1)
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