What is the exact length of arc ABC in circle E with a radius of 40 centimeters and an arc measure of 324 degrees?

To find the exact length of arc ABC in circle E, we can use the formula for the length of an arc:

Arc Length (L) = (θ / 360) * 2πr

Where:

• L = length of the arc
• θ = the central angle in degrees (in this case, 324 degrees)
• r = radius of the circle (in this case, 40 centimeters)

Plugging in the values:

L = (324 / 360) * 2π * 40

This simplifies to:

L = (0.9) * 2π * 40

Calculating further:

L = 0.9 * 80π

Therefore,

L = 72π

To express the answer in a decimal, you can approximate π:

L ≈ 72 * 3.14159 ≈ 226.19

Thus, the exact length of arc ABC is:

L = 72π centimeters

If you want an approximate length, it would be:

L ≈ 226.19 centimeters

So, whether you prefer the exact or approximate length, now you know how to calculate it!