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.

The radius is 3. Yielding a circumference of .

Begin by solving for the circumference of the circle. Use the area of the circle, which is given, and the equation for the area of a circle to determine the radius of the circle:

 = 

Divide both sides by .

 = 

Solve for :

The radius of the circle is 6. Now find the circumference.

Circumference is equal to 2 times the radius multiplied by .

Now that we have the circumference, divide by 6 to find the length of one of the slices of the circle:

The arc length of one of the slices of the circle is .

In order to solve this question, first calculate the length of each side of the room. 

The length of each side of the room is also equal to the length of the diameter of the largest circular rug that can fit in the room. Since , the circumference is simply

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

The equation is already in a circle equation, and the right side of the equation stands for r^2 → r² = 81 and r = 9

The area of a circle is πr², so the area of this circle is 81π.

If you answered that the whirlpool’s area is 18.84 feet and therefore fits, you are incorrect because 18.84 is the circumference of the whirlpool, not the area.

If you answered that the area of the whirlpool is 56.52 feet, you multiplied the area of the whirlpool by 1.5 and assumed that that was the correct area, not the legal limit.

If you answered that the area of the backyard was smaller than the area of the whirlpool, you did not calculate area correctly.

And if you thought the area of the backyard was 30 feet, you found the perimeter of the backyard, not the area.

The correct answer is that the area of the whirlpool is 28.26 feet and, when multiplied by 1.5 = 42.39, which is smaller than the area of the backyard, which is 56 square feet. 

The total area of both circles is π + π = 2π

Since the region overlaps, we cannot count it twice, so we must subtract it.

we get 2π – π = π

Using the Pythagorean Theorem, the diameter of the circle (also the diagonal of the square) can be found to be 4√2.  Thus, the radius of the circle is half of the diameter, or 2√2.  The area of the circle is then π(2√2)², which equals 8π.  Next, the area of the square must be subtracted from the entire circle, yielding an area of 8π-16 square inches.

The circumference of a circle = πd where d = diameter.  Therefore, this circle’s diameter must equal 16.  Knowing that diameter = 2 times the radius, we can determine that the radius of this circle = 8.  Halving the radius would give us a new radius of 4.  To find the area of this new circle, use the formula A=πr² where r = radius.  Plug in 4 for r.  Area will equal 16π.