The length of an arc of a circle equals 1/8 of the circle's circumference. What is the diameter of the circle if the length of the arc is 3.14?
1/8 the circumference is pi.
So, the whole circumference is 8pi
Since C = pi*d, d = 8
Would you mind showing us how you arrived at your answer please? I mean simplify to us old school folks!
To find the diameter of the circle, we need to know the length of the arc and the relationship between the length of an arc and the circumference of a circle.
Let's call the length of the arc "a" and the circumference of the circle "C". According to the given information, the length of the arc is 1/8 of the circle's circumference. Mathematically, we can write this as:
a = (1/8)C
We also know that the length of the arc is given as 3.14, so we can substitute the value of "a" into the equation:
3.14 = (1/8)C
To find the circumference, we can multiply both sides of the equation by 8:
8 * 3.14 = C
C = 25.12
Now that we know the circumference, we can use the formula for the circumference of a circle to find the diameter. The formula for the circumference of a circle is:
C = πd
Substituting the value of C, we have:
25.12 = πd
To find the diameter, we can divide both sides of the equation by π:
d = 25.12 / π
Using the approximate value of π as 3.14, we can calculate the diameter:
d ≈ 25.12 / 3.14
d ≈ 8
Therefore, the diameter of the circle is approximately 8 units.
To find the diameter of the circle, we need to use the relationship between the length of an arc and the circumference of a circle.
First, let's define the variables:
- L : Length of the arc
- C : Circumference of the circle
- r : Radius of the circle
- d : Diameter of the circle
We know that the length of an arc is equal to a fraction of the circle's circumference. In this case, we are given that the length of the arc (L) is equal to 1/8 of the circle's circumference (C). So, we can write this equation:
L = (1/8) * C
We also know that the circumference of a circle is given by the formula: C = 2πr, where π is approximately 3.14.
Substituting this into our equation, we have:
3.14 = (1/8) * 2πr
To find the diameter (d), we need to find the radius (r) first. Let's simplify the equation:
3.14 = (1/8) * 2 * 3.14 * r
3.14 = (1/4) * 3.14 * r
Now, we can cancel out π on both sides:
1 = (1/4) * r
To isolate r, we can multiply both sides by 4:
4 = r
Since the radius (r) is half the diameter (d), we can find the diameter by multiplying the radius by 2:
d = 2 * r = 2 * 4 = 8
Therefore, the diameter of the circle is 8 units.