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

Solution:

Diameter of a circle = 6 inches

The length of arc subtended by an angle measured in degrees is

Arc length = θ/360 × 2πr

Where θ is the central angle in degrees and r is the radius of the circle

Radius = diameter/2 = 6/2 = 3 inches

Now substitute the values in the formula

Arc length = 70/360 × 2π(3)

By further calculation

Arc length = 7/36 × 6π = 7π/6

Therefore, the length of the arc is 7π/6 inches.

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

Summary:

If the diameter of a circle is 6 inches, then the length of the arc subtended by an angle measuring 70° is 7π/6 inches.