Question

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

A) 9π feet
B) 2/9π feet
C)9/5π feet
D) 9/2π feet

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

The length of arc is
`L=(9)/(2)\pi` feet

D is correct

Explanation:

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

Formula:

`\theta=\frac{\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 = (\pi)/(180)* degree`

In radian
`=(\pi)/(180)* 81`

Substitute the value into formula

`(\pi)/(180)* 81=(L)/(10)`

`L=(810)/(180)\pi`

`L=(9)/(2)\pi` feet

Hence, The length of arc is
`L=(9)/(2)\pi` feet