Answered

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

A9π feet
B2/9π feet

C)9/5π feet

D9/2π feet

Verified Answer :

mollymollmoo99

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

isyllus

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