For this circle, a 50 degree central angle cuts off an arc of 6 in. What is the circumference?
50/360 of the circumference (x) is 6 in.
50x/360 = 6
The entire circumference is therefore
x = (360/50)*6 = 432 inches
To find the circumference of a circle, you can use the formula:
Circumference = 2πr
where π is approximately 3.14 and r is the radius of the circle.
In this case, we are given the length of the arc (6 in) and the measure of the central angle (50 degrees). We can use this information to find the radius of the circle and then calculate the circumference.
The formula to find the length of an arc, given the central angle and radius, is:
Arc Length = 2πr * (central angle/360)
In this case, the arc length is given as 6 in and the central angle is 50 degrees. Rearranging the formula, we have:
6 = 2πr * (50/360)
To solve for r, we can divide both sides by 2π * (50/360):
r = (6 / (2π * (50/360)))
Simplifying further:
r = (6 / (2π/7.2))
Using a calculator to evaluate this expression, we find:
r ≈ 2.17 in
Now that we have the radius, we can find the circumference using the formula:
Circumference = 2πr
Substituting the value of r:
Circumference = 2π * 2.17
Evaluating this expression, we find:
Circumference ≈ 13.6 inches
To find the circumference of a circle, we need to know the radius or the diameter.
In this case, since the question mentions a central angle and an arc, we can use the relationship between the central angle, the arc length, and the circumference of a circle.
The relationship is as follows:
Arc Length = (Central Angle / 360) * Circumference
We are given that the central angle is 50 degrees and the arc length is 6 inches. Let's plug these values into the equation:
6 = (50 / 360) * Circumference
To find the circumference, we can rearrange the equation and solve for it:
Circumference = 6 / (50 / 360)
Simplifying the expression:
Circumference = 6 * (360 / 50)
Circumference = 43.2 inches
So, the circumference of the circle is 43.2 inches.