for a circle of radius 8 feet find the arc length of a central angle of 60. leave your answer in Pi form.?

Question

please show work. thanks.

Answer 1

angle/360 * pi*Diameter is the arc length formula

so

60/360 * pi 16
8pi/3 feet is answer

Answer 2

Alternative answer to the first one.

Circumference is pi x diameter or pi x radius for half circumference. As we have the radius length of 8ft the half circle would measure around it's curved edge

pi x 8

As this is half the circle (180 deg) the 60 deg arc would be 1/3 so your formula would be

Radius (8 feet) x pi / 3 = Answer

Or

8 x 22/7 = 176/7
176/7 = 25 1/7
25 1/7 / 3 = 176/ 7 x 3 = 176/21
176/21 = 8 10/21 feet

You can decimalise it if you wish using 3.142 as pi

Answer 3

The formula is S=(r)(theta)
s= arc length
r= radius
theta=central angle

First step: Convert the central angle of 60 degrees into radians.

The formula is 60 degrees x Pi radians/ 180 degrees.

Multiply 60 degrees to Pi radians/ 180 degrees.
Notice that you can cross cancel 60 degrees and 180 degrees.
It will then reduce it to 3. Since the word degrees can also be crossed out, the final answer would be:

pi / 3 radians

Return to the original formula to find the arc length: s=(radius)(theta)

now you'll multiply the radius to pi/3 radians.

leaving you with: 8 pi/ 3 radians

Answer 4

Circumference is two times pi times the radius.
C = 2pi R
But that's for a whole circle.
60 degrees is one sixth of a circle. So:
(1/6) 2pi R = pi R/3