Question

How do I find the radius/x of a shaded region with it's area and/or angle measurement?

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Answer 1

r ≈ 9.8 feet

Explanation:

Formula of A Sector

• Area (Sector) = πr² × θ/360°

Substitute the given values in the formula to find r.

• 128 = 3.14 × r² × 152/360
• 40.76 = r² × 19/45
• r² = 1834.2/19
• r² = 96.54
• r ≈ 9.8 feet

Answer 2

`x \approx 9.823\ ft`

Explanation:

Remember that the area of a sector is defined as:

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

In this problem, we are given the area
`A`, and the angle
`\theta`. We can set up an equation to solve for the radius, which is x:

`A = (\theta)/(360^\circ)* \pi r^2\\128 = (152)/(360)* \pi r^2\\128 * (360)/(152) = \pi r^2\\(5760)/(19) = \pi r^2\\r = \sqrt{(5760)/(19 \pi)}\\r \approx 9.823`