Question

In a circle a radius 25 inches, a central angle of 35 degree will intersect the circle forming an arc of length

Answer 1

Arc length = angle/360 * pi*diameter

Length = 35/360 * pi*50

Length = 15.27 inches

Answer 2

The arc length of the circle(l) is given by:

`l = r \theta` ....[1]

where,

r is the radius of the circle

`\theta` is the angle in radian.

As per the statement:

In a circle a radius 25 inches, a central angle of 35 degree

⇒r = 25 inches

Use conversion:

1 degree = 0.0174533 radian

then

35 degree = 0.6108655 radian

⇒
`\theta = 0.6108655` radian

Substitute these values in [1] we have;

`l = 25 * 0.108655 = 15.2716375` inches

Therefore, in a circle a radius 25 inches, a central angle of 35 degree will intersect the circle forming an arc of length of 15.27 inches