A=(pir^(2)theta)/(360) The given equation can be used to find the area, A, of a sector of a circle of radius, r, where theta is the sector's central angle in degrees. Which of the following correctly shows the circle sector's radius in terms of the area of the sector and the central angle? Choose 1 answer: (A) r=sqrt((360 A)/(pi theta)) (B) r=(360 A)/(pi r theta) (c) r=sqrt((pi theta)/(360 A)) (D) r=(pi theta)/(360 Ar)

Question

A=(pir^(2)theta)/(360) The given equation can be used to find the area,  A, of a sector of a circle of radius,  r, where  theta is the sector's central angle in degrees. Which of the following correctly shows the circle sector's radius in terms of the area of the sector and the central angle? Choose 1 answer: (A)  r=sqrt((360 A)/(pi theta)) (B)  r=(360 A)/(pi r theta) (c)  r=sqrt((pi theta)/(360 A)) (D)  r=(pi theta)/(360 Ar)

Bytelearn · Accepted Answer

Write formula for area: Write down the given formula for the area of a sector of a circle. The given formula is A = (πr^2θ) / 360, where A is the area of the sector, r is the radius of the circle, and θ is the central angle in degrees.Isolate term r^2: Isolate the term r^2 in the formula to solve for r. To isolate r^2, multiply both sides of the equation by 360 and divide by πθ. 360A = πr^2θ r^2 = (360A) / (πθ)Solve for r: Solve for r by taking the square root of both sides of the equation. r = sqrt((360A) / (πθ))Check answer choices: Check the answer choices to see which one matches the derived formula. The correct answer choice that matches the derived formula is: r = sqrt((360A) / (πθ))

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