Question

The area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of 6pi The estimated value of pi is 3.14. The measure of the angle subtended by the arc is °. NextReset

Answer 1

A = pi r^2 78.5 = pi r^2 r = sqrt(78.5/pi) arc length in radians 6 pi cm / (sqrt(78.5/pi) cm/rad) = 3.77 rad or 3.77 rad / (pi rad / 180°) = 120° i assumed that you meant 6 pi cm for arc and the central angle is equal to subtended arc measure.

hope this helps !

Answer 2

The measure of the angle subtended by the arc is 216°.

Explanation:

Given : The area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of
`6\pi`. The estimated value of
`\pi` is 3.14.

To find : The measure of the angle subtended by the arc ?

Solution :

The area of a circle is 78.5 square centimeters.

We find the radius of the circle.

`A=\pi r^2`

`78.5=3.14* r^2`

`(78.5)/(3.14)=r^2`

`r=√(25)`

`r=5`

Now, The measure of the angle subtended by the arc formula in radian is given by,

`\theta=(s)/(r)`

Where,
`\theta` is the angle

r is the radius

s is the arc length

Substitute the value in the formula,

`\theta=(6\pi)/(5)`

Convert radian into degree,

Multiply radian by
`(180)/(\pi)`

So, In degree the angle is

`\theta=(6\pi)/(5)* (180)/(\pi)`

`\theta=216^\circ`

Therefore, The measure of the angle subtended by the arc is 216°.