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The circumference of a circle is #88pi# #cm#. What is the radius, and the length of an arc that is 40°?

Answer 1

Autumn Armstrong

Radius is #44#

The length of the arc is #2.76#

Given

#color(blue)("Circumference of the circle"=88pi#

We need to find the radius of the circle. For that we use the formula for the circumference of a circle

#color(brown)("Circumference of a circle"=2pir#

Where, #color(orange)(r="radius"#

#rarr2pir=88pi#

Cancel #pi# both sides

#rarr2cancelpir=88cancelpi#

#rarr2r=88#

Divide both sides by #2#

#rarrr=88/2#

#rArrcolor(green)(r=44#

Now we should find the length of the arc with angle #40^circ#

To find the length of arc, we use the formula for the length of arc

#color(brown)("Length of arc"=theta/360^circ*2pir#

Where, #theta# is the angle

#rarr40^circ/360^circ*2pi(44)#

#rarr1/9*88pi#

#rarr0.11*8*3.14#

#rArrcolor(green)(2.76#

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