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

Answer:

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

Step-by-step 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.

$A=\pi r^2$

$78.5=3.14\times r^2$

$\frac{78.5}{3.14}=r^2$

$r=\sqrt{25}$

$r=5$

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

$\theta=\frac{s}{r}$

Where, $\theta$ is the angle

r is the radius

s is the arc length

Substitute the value in the formula,

$\theta=\frac{6\pi}{5}$

Convert radian into degree,

Multiply radian by $\frac{180}{\pi}$

So, In degree the angle is

$\theta=\frac{6\pi}{5}\times \frac{180}{\pi}$

$\theta=216^\circ$

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

Answer 2

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 !