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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

User Chmac
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2 Answers

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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 !
User Gagarine
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Answer:

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°.

User Sascha Gottfried
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