Question

If the diameter of a circle is 6 inches, how long is the arc subtended by an angle measuring 70°?

Answer 1

C = πD = π6in

Arc = D * 70°/360° = 3.1416*6*7/36=3.67 in

Answer 2

Length of arc of a circle is given by:

`L = r \cdot \theta` .....[1]

where

L is the length of an arc

r is the radius of the circle.

As per the statement:

Diameter of the circle(D) = 6 inches.

we know that:

D =2r

6 = 2r

Divide both sides by 2 we get;

3 = r

or

r = 3 inches

We have to find the long arc arc subtended by an angle measuring 70°.

Substitute the value of r = 3 inches and
`\theta = 70^(\circ)` in [1] we have;

`L =3 \cdot 70`

Simplify:

L = 210 inches

Therefore, 210 inches long is the arc subtended by an angle measuring 70 degree.