Question

if the length of an arc of a circle is 6π and radius is 6cm find it's central angle​

Answer 1

Answer:

Arc length of the Circle : Area of the Sector = Perimeter of the Circle :Area of the Circle

Let the radius of the circle be 'r'.

Hence, 20:60=2πr:πr

2

1:3=2:r

r=6 (Product of Means = Product of Extremes)

Therefore, Diameter=2r=12cm

Answer 2

Given: The length of an arc of a circle = 6$\pi$

           The radius of the circle = 6 cm

To find: The central angle subtended by the arc

Solution: The formula fpr the length of an arc is given by x/360 × 2$\pi$r (where r is the radius of the circle and x is the angle subtended by the arc at the center of the circle).

So according to the question,

x/360 × 2$\pi$r = 6$\pi$

⇒ x/360 × 2$\pi$ × 6 = 6$\pi$

⇒ x/360 × 2 = 1

⇒ x = 360/2

⇒ x = 180°

Therefore, the central angle = 180°.

Answer: 180°