Question

A circle has a central angle measuring StartFraction 7 pi Over 10 EndFraction radians that intersects an arc of length 33 cm. What is the length of the radius of the circle? Round your answer to the nearest whole cm. Use 3.14 for Pi.

Answer 1

15

Explanation:

Answer 2

15 cm.

Explanation:

It is given that,

Central angle
`=(7\pi)/(10)`

Arc length = 33 cm

Formula for arc length :

`s=r\theta`

where, s is arc length, r is radius and
`\theta` is central angle in radian.

Substitute s=33 and
`\theta=(7\pi)/(10)` in the above formula.

`33=r\left((7\pi)/(10)\right)`

Multiply both sides by 10.

`330=7\pi r`

Divide both sides by
`7\pi`.

`(330)/(7\pi)= r`

Put
`\pi=3.14`

`(330)/(7(3.14))= r`

`15.0136= r`

`r\approx 15`

Therefore, the radius of the circle is 15 cm.