well, recall that a circle has a total of 360°.
now, that central angle of 60°, has an arc of 40 units.
well, how many 60° are there in 360°? 360/60 = 6.
well, there are 6 of those, and since each has a 40 units arc, there should also be six 40 units arcs for the whole circle, namely its circumference, 6*40.
The required circumference of the circle is 240 cm.
Given that,
Length of ab the minor Arc is 40 cm what is the circumference of C is to be determined.
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²,
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Here,
Angle = arc / radius
60 * π/180 = 40/radius
radius = 120/π
Circumference of the circle = 2π * radius
= 2π * 120/π
= 240 cm
Thus, the required circumference of the circle is 240 cm.
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