The figure shows a circle with a shaded sector whose area is one hundred twenty five sixths times pi units squared. The shaded circle sector has a central angle of 300 degrees.The circle shown has a sector with area   and central angle of  . What is the area of the circle?Choose 1 answer:Choose 1 answer:(Choice A)    A  (Choice B)    B  (Choice C)    C  (Choice D)    D Show Calculator

To find the area of the circle, we need to use the information given about the shaded sector.

First, we are told that the area of the shaded sector is one hundred twenty five sixths times pi units squared. This can be written as (125/6)π.

Next, we are given that the central angle of the shaded sector is 300 degrees.

To find the area of the entire circle, we can use the formula for the area of a sector:

Area of sector = (θ/360) * π * r^2

Where θ is the central angle and r is the radius of the circle.

In this case, we know that the central angle is 300 degrees. So, we can substitute this value into the formula:

(125/6)π = (300/360) * π * r^2

Simplifying the equation, we have:

(125/6) = (5/6) * r^2

To solve for r^2, we can multiply both sides of the equation by 6/5:

r^2 = (125/6) * (6/5)

r^2 = 25/2

Taking the square root of both sides, we find:

r = √(25/2)

Simplifying further, we have:

r = √(25/2) = √(25) / √(2) = 5 / √(2) = (5√2) / 2

Now that we have the radius of the circle, we can find its area using the formula:

Area of circle = π * r^2

Substituting the value of r, we have:

Area of circle = π * ((5√2) / 2)^2

Simplifying the equation, we get:

Area of circle = π * (25/2)

Area of circle = (25/2)π

Therefore, the area of the circle is (25/2)π.