Question

Find the are length of the partial circle.

Either enter an exact answer in terms of π or use 3.14 for π and enter your
answer as a decimal.
units

Answer 1

10.99 units

Explanation:

The formula to find the arc length (
`\sf s`) of a circle, given the radius (
`\sf r`) and the central angle (
`\sf \theta`) in degrees, is:

`\sf s = (\theta)/(360) * 2 \pi r`

Given that the radius (
`\sf r`) is 7 units and the central angle (
`\sf \theta`) is 90°, we can substitute these values into the formula:

`\sf s = (90)/(360) * 2 \pi * 7`

Now, calculate the arc length:

`\sf s = (1)/(4) * 14 \pi`

`\sf s = (14)/(4) \pi`

`\sf s = (7)/(2) \pi`

If we prefer a decimal approximation, we can use 3.14 for
`\sf \pi`:

`\sf s \approx (7)/(2) * 3.14`

`\sf s \approx 10.99`

Therefore, the arc length of the partial circle is either
`\sf (7)/(2) \pi` units or approximately 10.99 units (rounded to two decimal places).