If the radius of a circle is 10 feet, how long is the arc subtended by an angle measuring 81°?

Solution:

We know that

The perimeter of a circle = 2πr

Where r is the radius of the circle

Here

A complete circle is made by 360° angle = 2πr

The arc length made by 1° angle = 2πr/360°

The arc length made by 81° angle = [2πr/360°] × 81°

By further calculation

= [(2 × π × 10)/360°] × 81°

So we get

= 14.14 feet

Therefore, arc length subtended by 81° angle is 14.14 feet.

If the radius of a circle is 10 feet, how long is the arc subtended by an angle measuring 81°?

Summary:

If the radius of a circle is 10 feet, the length of the arc subtended by an angle measuring 81° is 14.14 feet.