Find the diameter of a circle with an arc length of 32 cm and a subtended angle of 72 degrees

yeah the diameter is actually 165/π cm just multiply it next time glad i can help

To find the diameter of a circle with an arc length of 32 cm and a subtended angle of 72 degrees, you can use the following formula:

Arc Length = (Angle / 360) * (2 * π * Radius)

In this case, we know the arc length is 32 cm and the angle is 72 degrees. We need to find the radius and then the diameter.

Step 1: Convert the angle from degrees to radians.
To convert degrees to radians, you can use the formula:
Radians = (Degrees * π) / 180

Substituting the given angle:
Radians = (72 * π) / 180
Radians = 1.26 radians (approx)

Step 2: Rearrange the formula to solve for the radius.
Arc Length = (Angle / 360) * (2 * π * Radius)
32 = (1.26 / 360) * (2 * π * Radius)
32 = (0.35) * (2 * π * Radius)

Step 3: Solve for the radius.
Divide both sides of the equation by 0.35:
Radius = 32 / (0.35 * 2 * π)
Radius ≈ 45.71 cm (approx)

Step 4: Find the diameter.
Double the radius to get the diameter:
Diameter = 2 * Radius
Diameter ≈ 2 * 45.71
Diameter ≈ 91.42 cm

Therefore, the diameter of the circle is approximately 91.42 cm.

To find the diameter of a circle with an arc length of 32 cm and a subtended angle of 72 degrees, we can use the formula:

Arc Length = (Angle/360) * (2 * π * radius)

Where:
- Arc Length is the length of the arc
- Angle is the subtended angle in degrees
- π (Pi) is a mathematical constant approximately equal to 3.14159...
- Radius is the distance from the center of the circle to any point on the circumference

First, we need to convert the angle from degrees to radians, as the formula requires the angle in radians. The conversion formula is:

Angle in Radians = (Angle in Degrees * π) / 180

For this problem, the angle in radians is:

Angle in Radians = (72 * π) / 180

Next, we rearrange the formula to solve for the radius:

Radius = (Arc Length) / [(Angle/360) * (2 * π)]

Plugging in the given values:

Radius = 32 / [(72 * π) / 180 * (2 * π)]

Simplifying the equation:

Radius = 32 / [(72 * π) / 180 * 2 * π]
Radius = 32 / [(72 / 180 * 2)]
Radius = 32 / [(0.4 * 2)]
Radius = 32 / 0.8
Radius = 40 cm

Finally, we can find the diameter by doubling the radius:

Diameter = 2 * Radius
Diameter = 2 * 40
Diameter = 80 cm

Therefore, the diameter of the circle is 80 cm.

72° = (π/180)(72) radians = 2π/5 radians

arc = rØ
32 = 2π/5 r
r = 80/π

so the diameter is 160/π cm or appr 50.9 cm

or

72/360 = 32/(2πr)
144πx = 32(360)
x = 80/π , as above