find the area of a seclor of circle of radius 28cm
and central angle 45°
Answers
r= 28cm
central angle (theta)= 45
area of sector=theta/360*pi*r*r
=45/360*22/7*28*28
308cm²
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Given :-
◉ Radius of circle, r = 28 cm
◉ angle between the two radii, θ = 45°
To Find :-
◉ Area enclosed by the two radii and the arc.
Solution :-
First, Convert the angle into radians.
⇒ θ = 45 × π / 180 rd.
⇒ θ = π / 4 rd.
Now,
⇒ Area = 1/2 r²θ
⇒ Area = 1/2 × 28 × 28 × π / 4
⇒ Area = 14 × 7 × π
⇒ Area = 14 × 7 × 22/7 [ take, π = 22/7 ]
⇒ Area = 14 × 22
⇒ Area = 308 cm²
Hence, Area of the sector is 308 cm².
Some Information :-
☛ 1 radian is the ratio of the arc of length the same as the radius of the circle and the radius itself. It is a constant for every circle.
☛ Convert Degrees into Radians:-
Multiply the given value by π/180
☛ Convert Radians into Degrees:-
Multiply the given value by 180/π
☛ To find the length of the arc, use the given formula:
l = rθ
Where, r = radius, l = length, θ = angle between the two radii ( in radians )