What is the area and radius of a circle when the circumference is 18 inches ?

## What is the area and radius of a circle if the circumference is 18 inches ?

# 2 Answers

Amanda,

The formula for the circumference of a circle is C=2∏r, in which r=radius. To find the radius, then, we insert 18 in for the circumference. So 18=2∏r. Solving for r gives 9/∏, or approximately 2.86 inches.

Now that we have the radius, we can find the area. The formula for the area of a circle is A=∏r^{2}. So inserting 9/∏ for r gives us A=∏(9/∏)^{2}. Then A=∏(81/∏^{2}). Simplifying gives A=81/∏, or approximately 25.78 inches.

Hey Amanda -- sorry about the late answer!

Circumference (C) is "the walk-around": C is about 3x diameter or 6x radius (adjust by 5% to be closer) ... for your example, radius (r) is C/6 or 3" (subtract 5% or 0.15 to get 2.85").

For Area (A), first visualize a square: radius (r) would be half a side ... Area of square is 2r*2r or 4r*r ... Next, visualize a square-shaped diamond inside the 1st box -- diamond corners touching North, South, East, West. Area of inside diamond is 1/2 the outer box or 2r*r ... Finally, draw a circle touching the inside edges of the 1st outer box ... The circle area is BETWEEN the outer box area 4r*r and the inner diamond area of 2r*r ... Circle area would be 3r*r or 3*3*3 or 27 sq.in. (subtract 5% or 1.35 to get 25.65 sq.in.)

CIRCLE SUMMARY: "Walk-around" (C) is 3x the "walk-across" or 6x the radius (add 5% tip for closer C) ... Area is 3x radius squared or 3/4 of the diameter squared (add a 5% tip for closer Area)

Best wishes, ma'am :)