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Find the perimeter and area of a sector which has radius 8 cm and a sector angle of 66 C

User Kawty
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Explanation:

a sector of a circle is like a piece of pie or pizza. a kind of triangle, but with the baseline not being a straight line but a round piece (arc) of the circle circumference.

it represents a piece of the whole circle. its area and the length of the arc a "baseline" have the same ratio to the full circle's area and circumference, as the given angle of the sector has with the full circle's 360°.

so, the sector ratio is

66/360 = 33/180 = 0.183333333...

the area of a circle is

pi×r²

with r being the radius.

the area of our sector is therefore

pi×8² × 33/180 = pi×64 × 33/180 =

= 36.8613538... cm²

the circumference (the full arc) around the whole circle is

2×pi×r

again, r is the radius.

the arc length of our sector is

2×pi×8 × 33/180 = 9.215338451... cm

the perimeter of our sector is now that arc length plus two times the radius (the "legs" of the "round triangle") :

9.215338451... + 2×8 = 25.21533845... cm

User Parashuram
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