Question

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

Answer 1

81 degrees
1 degree = 2 pi / 360
81 degrees = 162 pi / 360
=9 pi / 20

L (arc) = radius x angle
= 10 x 9 pi / 20
90 pi /20
9/2 pi : D

The answer is D

Answer 2

Answer:

The length of arc is $L=\dfrac{9}{2}\pi$ feet

D is correct

Step-by-step explanation:

Given: If the radius of a circle is 10 feet and arc subtended by an angle measuring 81°

Formula:

$\theta=\dfrac{\text{Length of arc}}{\text{Radius}}$

where,

Length of arc = L?

Radius of circle, R= 10 feet

Central angle, Ф=81°

First we will change 81 degree to radian

$Radian = \dfrac{\pi}{180}\times degree$

In radian $=\dfrac{\pi}{180}\times 81$

Substitute the value into formula

$\dfrac{\pi}{180}\times 81=\dfrac{L}{10}$

$L=\dfrac{810}{180}\pi$

$L=\dfrac{9}{2}\pi$ feet

Hence, The length of arc is $L=\dfrac{9}{2}\pi$ feet