The length of an arc of a circle (s) is given by the equation: s= r0 Where r is the radius of the circle and 0 is the angle, in radians, subtended to the centre of the circle.  Find the length of...

The length of an arc of a circle (s) is given by the equation:

s= r0

Where r is the radius of the circle and 0 is the angle, in radians, subtended to the centre of the circle. 

Find the length of the arc traced by a point on a bicycle wheel, of radius 30 cm as the wheel is rotated through an angle of 45°

Asked on by dorotapog

3 Answers | Add Yours

steveschoen's profile pic

steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

The formula is:

s = r*theta

Where s is the length of the arc, r is the radius, and theta is the angle measured in radians.

We are given r = 30 cm.  For the angle of 45 degrees, we have to convert that to radians.  There are various conversions for this.  We will use:

180 degrees = pi radians

So, setting up for the converstion:

180 degrees = pi radians
 45 degrees  =     x

Cross multiplication:

180 x = 45pi

x = 45pi/180 = pi/4

So, the angle is pi/4 radians.

Plugging in 30 and pi/4, we get:

s = 30 * pi/4

= 7.5*pi

= 23.562 cm

Educator Approved

Educator Approved
Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

This question is asking you to plug in what you know into the given formula. 

`s = rtheta`  where s is arc length, r is radius, and `theta` is the angle in radians. 

You are given the angle in degrees but since 45 is on the unit circle, this is an easy conversion. 45 corresponds to `pi/4`

`s = 30 * (pi/4)`

`s = (15pi)/2cm`

Educator Approved

Educator Approved
shmindle's profile pic

shmindle | Student, Grade 11 | (Level 2) Honors

Posted on

First, you would need to convert 45° into radians.  To do this, multiply it by (pi/180°), to get .25pi radians.  

Using the equation s=r0, the radius is 30 cm and the radians is .25pi radians.

multiply these together, (pi is approximately 3.14), to get 23.56 cm for the length of the arc. 

` `

` `

` ` ` `

` `

We’ve answered 318,929 questions. We can answer yours, too.

Ask a question