This question asks you to apply the concept of area in finding both the area of a circle and square. Since the cirlce is inscribed in the square, we know that its diameter (two times the radius) is the same length as one side of the square. Since we are given the radius, , we can find the area of both the circle and square.

Square:

This gives us the area for the entire square.

The bottom half of the square has area .

Now that we have this value, we must find the area that the circle occupies. The area of a circle is given by .

So the area of this circle will be .

The bottom half of the circle has half that area:

Now that we have both our values, we can subtract the bottom half of the circle from the bottom half of the square to give us the shaded region:

To find the area of a circle with a given radius, use the formula:

To solve, simply use the formula for area of a circle.

Since the question gives us the value of the radius, we can substitute 8 in for the radius to solve for the area.

Thus,

To solve, simply use the formula for the area of a circle.

In this particular case, substitute one in for the radius in the following equation.

Thus,

We can use the fact that the longest chord of a circle is its diameter.

In other words, this circle has a diameter of inches, meaning a radius of inches.

From there, finding the area is straightforward:

If the circumference is , then since  we know . We further know that , so 

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.