The area of the circle with a radius of 6 ft has been [tex]\rm \bold{36\;\pi \;ft^2}[/tex]. Thus option C is correct. The area of the circle with a circumference [tex]\rm \bold{7\pi}[/tex] has been 12.25[tex]\rm \bold{\pi \;m^2}[/tex]. Thus, option B is correct.
1. The circumference of the circle and the diameter of the circle ratio can be given by the Archimedes concept.
The ratio of the circumference to the diameter of a circle has been a constant.
The value for the ratio has been equivalent to the value of pi.
Thus, [tex]\rm \dfrac{circumference}{diameter}\;=\;\pi[/tex]
We know that, diameter = 2 times of radius
Diameter = 2 [tex]\times[/tex] radius
Substituting D with 2r
Circumference = [tex]\pi[/tex] 2r
C = 2[tex]\pi[/tex]r.
Thus the circumference of the circle can be given by the relationship between the circumference and the diameter by dividing the length of the circumference and length of the diameter. Use this quotient to set up an equation to show the ratio of the circumference over the diameter equals to [tex]\pi[/tex] . Then rearrange the equation to solve for the circumference. Substitute 2 times the radius for the diameter. Thus option A is correct.
2. While deriving the area of the circle with the inscription of a polygon, the area of the polygon has n corresponding to h.
So, with the increase in n there has been increased in the h approaching r so that rhrh approaches [tex]\rm r^2[/tex]. Thus statement B is true.
3. Area of the circle has been given by:
Area = [tex]\pi[/tex][tex]\rm r^2[/tex]
Area = 3.14 [tex]\rm \times\;(6)^2[/tex]
Area = 3.14 [tex]\times[/tex] 36 sq. ft
Area = 36[tex]\pi[/tex] [tex]\rm ft^2[/tex].
The area of the circle with a radius of 6 ft has been [tex]\rm \bold{36\pi ft^2}[/tex]. Thus option C is correct.
4. Circumference = [tex]\pi[/tex] [tex]\times[/tex] diameter
7[tex]\pi[/tex] = circumference
Diameter = 7 m.
Radius = 3.5 m
Area = [tex]\rm \bold{\pi r^2}[/tex]
Area = [tex]\rm \pi \;(3.5)^2[/tex]
Area = 12.25[tex]\rm \bold{\pi \;m^2}[/tex].
The area of the circle with a circumference [tex]\rm \bold{7\pi}[/tex] has been 12.25[tex]\rm \bold{\pi \;m^2}[/tex]. Thus, option B is correct.
For more information about the circumference and area of a circle, refer to the link:
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