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

The measure of the angle is

Step-by-step explanation:

step 1

Find the radius of the circle

The area of the circle is equal to

we have

substitute and solve for r

step 2

Find the circumference of the circle

The circumference of the circle is equal to

we have

Substitute

step 3

Find the measure of the angle by an arc length of 6 cm

we know that

The circumference of a circle subtends a central angle of 360 degrees

So

by proportion

The measure of the angle subtended by the arc is 68.8°

Step-by-step explanation:

Formula for calculating length of an arc is expressed as:

Length of an arc = theta/360×2πr

Where theta is the angle subtended by the arc

r is the radius of the circle

To get the radius r;

Given Area of the circle to be 78.5cm²

Since area = πr²

78.5 = πr²

78.5 = 3.14r²

r² = 78.5/3.14

r² = 25

r =√25

r = 5cm

This radius of the circle is 5cm

Remember that

Length of an arc = theta/360° × 2πr

6 = theta/360 × 2(3.14)(5)

6 = 31.4theta/360

2160 = 31.4theta

theta = 2160/31.4

theta = 68.8°

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