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A sector of a circle of radius 6 cm subtends an angle of 105° at the centre. Calculate the:
(i) perimeter;
(ii) area;
of the sector.
[Take π = 22/7]
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(i) The perimeter of this sector is the sum of the arc length plus twice the length of the radius.
The arc length is the circle circumference multiplied by the ratio of angles = .
So, we write for the atc length
= = = = = 11 cm.
Then the perimeter of the sector is 11 + 2*6 = 23 cm.
(ii) The area of the sector is = part of the area of the circle
area of the sector = = = = 11*3 = 33 cm^2
using the given approximation.
Solved.