Question

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

Answer 1

Radius is `44`

The length of the arc is `2.76`

Explanation:

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`