Question

in a circle of diameter 60m, the length of a chord is 30m. Then the length of the major arc is
a) 150.1 m b) 157.1 m
c) 152.1 m
d) 154.1m​

Answer 1

Using the formula, half of the chord length should be the radius of the circle times the sine of half the angle. Multiply this result by 2. Notice that the length of the chord is almost 2 meters, which would be the diameter of the circle.

Answer 2

The length of the major arc is (b) 157.1 m.

Given: The diameter of the circle = 60 m

The length of the chord = 30 m

To Find: The length of the major arc.

Solution:

The diameter of the circle is = 60 m

So, the radius of the circle = 60 / 2 = 30 m

Also, the length of the chord is = 30 m

So, we can visualize that the radii and the length of the chord form an equilateral triangle with each side equal to 30 m.

Thus, the angle formed by the circle at the center = 60°

The length of the chord can be found by the formula = Ф × (π/180°) × r

Where Ф = angle formed at the center by the chord, r = radius.

So, the length of the chord = 60 × ( π / 180° ) × 30

                                               = 10π

The total length of the perimeter = 2πr = 60π

Thus, the length of the major axis = ( 60π - 10π ) m

                                                           = 50π m

                                                           = 157.1 m

Hence, the length of the major arc is (b) 157.1 m.

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