Answer:
The measure of the angle is [tex]68.79\°[/tex]
Step-by-step explanation:
step 1
Find the radius of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]A=78.5\ cm^{2}[/tex]
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]78.5=(3.14)r^{2}[/tex]
[tex]r^{2}=78.5/(3.14)[/tex]
[tex]r=5\ cm[/tex]
step 2
Find the circumference of the circle
The circumference of the circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=5\ cm[/tex]
[tex]\pi =3.14[/tex]
Substitute
[tex]C=2(3.14)(5)[/tex]
[tex]C=31.4\ cm[/tex]
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
[tex]\frac{31.4}{360}=\frac{6}{x}\\ \\x=360*6/31.4\\ \\x=68.79\°[/tex]
Answer:
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°
