Below is the figure referenced; note that the hexagon is divided by its diameters.

The hexagon is divided into six equilateral triangles; the length of each side is equal to the radius of the hexagon, and, consequently, the radius of the circle. The regular hexagon has perimeter 120, so the length of each congruent side is. The radius of the hexagon, and of the circle, is 20 also.

The area of the circle can be found using the area formula, setting:

Below is the figure referenced; note that the hexagon is divided by its diameters, and that an apothem - a perpendicular segment from the center to one side - has been drawn.

The hexagon is divided into six equilateral triangles. The regular hexagon has perimeter 120, so the length of each congruent side is.

Specifically,is a 30-60-90 triangle.is the midpoint of, so

By the 30-60-90 Theorem, sinceandare the short and long legs of a right triangle,

.

This is the apothem of the hexagon; this is also the radius of the circle.

The area of the circle can be found using the area formula, setting:

To convert degrees to radians, we need to remember the following formula.

.

Now lets substitute for degrees.

一个立方体的体积的方程

.

If V= 216, then s = 6.

When a circle is circumscribed by a square the diameter of the circle is equal to the length of one side of the square. In this case, one side of the square is equal to 6; therefore the diameter of the circle is also 6. We can find the area of a circle with the equation

and since the radius is equal to half the diameter:

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 isA=πr².

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

我们分了theπand are left with 13 =r².

We take the square root ofrto find thatr= √13.

We find the circumference of the circle with the formulaC= 2πr.

We then plug in our values to findC= 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.

花园由一个长方形的形状d 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 isπd, orπ√5.

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.