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 9 π feet C) 9 5 π feet D) 9 2 π feet

Answer 1

Option D.
`(9)/(2)\pi \ ft`

Explanation:

step 1

Find the circumference of the circle

The circumference of a circle is equal to

`C=2\pi r`

we have

`r=10\ ft`

substitute

`C=2\pi (10)=20\pi\ ft`

step 2

we know that

360° subtends the complete circle of length 2πr.

so

By proportion

Find the length of the arc subtended by an angle measuring 81°

`(20\pi )/(360)= (x)/(81)\\ \\x=20\pi (81)/360\\ \\x= (9)/(2)\pi \ ft`