Know that the formula for circumference is , where C is the circumference and D is the diameter.  It is given that the diameter is 12 inches.  Therefore, the circumference is 

Because the circle is circumscribed around the square, the diagonal of the square is the same as the diameter of the circle. So to find the diagonal we use the Pythagorean Theorem:

So the equation to solve becomes or

The perimeter, or circumference, of the circle is given by or

The perimeter of the rink runs along the outside of the combined shapes. The two outer edges of the rectangle are   each, so   of the perimeter consists of those two sides.

The two semi-circles that form the remainder of the perimeter, and can be considered two halves of one circle. The diameter of the circle would be . The circumference of the circle would account for the outer edges of the two semi-circles in the ice rink. Find the circumference of the circle with the formula  as follows.

Finally, add this circumference that accounts for the semi-circles to the length of the two sides formed by the rectangle to find the total perimeter of the rink.

The formula for  the area of a circle is πr². For this particular circle, the area is 81π, so 81π = πr². Divide both sides by π and we are left with r²=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.

The formula for the area of a circle is A = πr².

We are given the area, and by substitution we know that 13π = πr².

We divide out the π and are left with 13 = r².

We take the square root of r to find that r = √13.

We find the circumference of the circle with the formula C = 2πr.

We then plug in our values to find C = 2√13π.

First you must draw the diagram. The diagonal of the rectangle is also the diameter of the circle. The diagonal is the hypotenuse of a multiple of 2 of a 3,4,5 triangle, and therefore is 10.
Circumference = π * diameter = 10π.

The shape of the garden consists of a rectangle and two semi-circles. Since they are building a fence we need to find the perimeter. The perimeter of the length of the rectangle is 24. The perimeter or circumference of the circle can be found using the equation C=2π(r), where r= the radius of the circle. Since we have two semi-circles we can find the circumference of one whole circle with a radius of 4, which would be 8π.

We first must calculate the distance between these two points. Recall that the distance formula is:√((x₂ - x₁)² + (y₂ - y₁)²)

For us, it is therefore: √((4 - 2)² + (6 - 5)²) = √((2)² + (1)²) = √(4 + 1) = √5

If d = √5, the circumference of our circle is πd, or π√5.

To find the circumference of a circle, multiply the circle's diameter by pi (3.14).

If the radius is 18 inches, the diameter is 3 feet. The circumference of the tire is therefore 3π by C=d(π). After 200 revolutions, the tire and car have gone 3π x 200 = 600π feet.