Question

5 A circle has a radius of 12 in. Find an exact value for each measurement. (Hint: Use arc length formula to find angle)

a) an arc length with a central angle of 90°:
b) the area of a sector with a central angle of 90°:​

Answer 1

`(a)\ L = 18.84` --- arc length

`(b)\ A = 113.04` --- sector area

Explanation:

Given

`r = 12`

`\theta = 90`

Solving (a): The arc length

This is calculated using:

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

So, we have:

`L = (90)/(360) * 2* 3.14 * 12`

`L = 0.25* 2* 3.14 * 12`

`L = 18.84`

Solving (b): The sector area

This is calculated using:

`A = (\theta)/(360) * \pi r^2`

So, we have:

`A = (90)/(360) * 3.14 * 12^2`

`A = 0.25 * 3.14 * 12^2`

`A = 113.04`