Question

This is the first year Janis is playing softball. She has been practicing her batting. On her last swing the bat made an arc with a radius of 48 inches and swept through 255° of rotation. Assuming the arc is circular, what is the distance the tip of the bat travels in inches in terms of pi? How many feet is this in terms of pi?

Answer 1

Answer:

• a) 60π inches

• b) 5π feet

Explanation:

The arc length of a circular sector is related to the swept angle by the proportion:

       

        $\dfrac{arc\text{ }length}{2\pi \cdot radius}=\dfrac{angle}{360\º}$

Here you have:

• arc length: ?
• radius: 48 inches
• angle: 225º

Substitute and solve for the arc length:

In inches:

       $arc\text{ }length=\dfrac{225\º}{360\º}\times 2\pi (48in)}=60\pi$   inches

Convert to feet:

Use the conversion factor: 1 feet = 12 inches

           $60\pi\text{ }in\times\dfrac{1ft}{12in}=5\pi ft$