From: Alex
Grade: 6 (middle)
Student

How do you find the circumference of a circle if you only know the radius and the square feet or inches of the circle if the radius is 18 inches, If done in inches do you multiply by 12 to get the square feet?

Thank You

Alex

Hi Alex

The circumference of a circle is a little more than three times its diameter. To convince yourself of this find a circular lid from a take-out coffee cup and a twist tie. Use the twist tie to determine the diameter of the circle. (Put the end of the tie on the edge of the circle and lay it across the circle to the opposite edge so that the tie passes over the centre of the lid.) Bend back or cut off any extra twist tie. Now bend the twist tie so that it has the same bend as the circle edge. Make 3 more the same length. Mark a start point on the edge of the circle and see how many of these twist ties it will take to just go around the outside of the circle. It will take just over 3. So you can see that the circumference of that circle is just over 3 diameters.
     The circumference of a circle is given by C = pi x d where pi is a number a little greater than 3 (pi is approximately 3.14159) and d is the diameter which is the length of a line drawn from one edge, through the centre, to the opposite edge. The diameter is twice the radius. So if you know the radius you can multiply it by 2 to obtain the diameter. You can then multiply this answer by pi which you will probably find on your calculator to obtain the circumference. Thus for your circle of radius 18 inches the circumference is 2 x 18 x pi inches or approximately 113 inches. There are 12 inches in 1 ft. so if you want to change 113 inches to feet you need to divide by 12. You divide because it takes fewer feet to do the same job as 113 inches (a foot is bigger than an inch). You don't need to work with square inches and square feet because circumference is the distance around and is a length (not an area).
     However, if you are working with area, you will need to work with square feet and square inches. Since 1 foot = 12 inches,
1 square foot = 1 foot x 1 foot = 12 inches x 12 inches = 12² square inches. Thus to change from square feet to square inches you need to multiply by 12² = 144.
     The area of a circle is given by pi x r² where r is the radius and thus for your circle of radius 18 inches the area is pi x 18² or approximately 1018 square inches. If you want this in square feet then, since feet are larger than inches, you need to divide by 144.

Cheers
Jack and Harley