The city is building a new roundabout in order to correct a traffic flow issue at some of its intersections. Due to safety regulations, the inner circle must have a diameter of 9 ft. When construction is complete, they plan to cover this area with grass. How much sod do they need to cover the inner circle of the roundabout?

Write a paragraph, following the RACE format, to explain how you calculate this answer.

Answer:

I don’t know

Step-by-step

StOp

The total sod needed to cover the inner circle of the roundabout is given by C = 28.27 feet

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the city be building a new roundabout in order to correct a traffic flow issue at some of its intersections

Now , the diameter of the inner circle be d = 9 feet

So , the radius of the inner circle , r = d/2

On simplifying , we get

The radius of the inner circle r = 4.5 feet

Now , the amount of sod do they need to cover the inner circle of the roundabout = circumference of the roundabout

The circumference of the circular roundabout C = 2πr

The circumference of the circular roundabout C = 2π ( 4.5 )

The circumference of the circular roundabout C = 9π feet

The circumference of the circular roundabout C = 28.27 feet

Hence , the amount of sod for the roundabout is 28.27 feet

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