in a circle of radius 28cm,an arc subtends an angle of 45 degrees at the circle.Find the length of the arc and using find the area of the sector
Answers
Step-by-step explanation:
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Given : A circle of radius 28cm,
an arc subtends an angle of 45 degrees at the circle.
To Find :
the length of the arc
the area of the sector
Solution:
Radius r = 28 cm
Sector angle ( arc angle) = 45°
Length of arc = ( arc angle in deg/ 360° ) * 2πr
= (45° / 360°) 2 * (22/7) * 28
= (1/8) * 2 * 22 * 4
= 22 cm
the length of the arc is 22 cm
Area of the sector = ( sector angle in deg/ 360°) π r²
= (45° / 360°) (22/7) * (28)²
= (1/8) * 22 * 4 * 28
= 11 * 28
= 308 cm²
the area of the sector is 308 cm²
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