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.

The area of the circle is (30/2)²*3.14 (π) = 706.5, since the shaded region is simply the area difference between the circle and the star, it’s 706.5-345 = 361.5

The original radius would be 4, making the new radius 8 and by the area of a circle (A=π(r)²) the new area would be 64π.

The area of a circle is πr². 

The diameter of the first circle = 6” so radius of the first circle = 3” so the area = π * 3² = 9π in²

The radius of the second circle = 8” so the area = π * 8² = 64π in²

The area of the interstitial space = area of the first circle – area of the second circle.

Area = 64π in²  - 9π in² = 55π in²

The area of a circle is A=πr². Since the radius was tripled 144π =π(3r)². Divide by π and then take the square root of both sides of the equal sign to get 12=3r, and then r=4. The diameter (d) is equal to twice the radius so d= 2(4) = 8.

We know that the equation for the area of a circle is π r². To solve this problem, we pick radii for Circles A and B, making sure that Circle A’s radius is three times Circle B’s radius, as the problem specifies. Then we will divide the resulting areas of the two circles. For example, if we say that Circle A has radius 6 and Circle B has radius 2, then the ratio of the area of Circle A to B is: (π 6²)/(π 2²) = 36π/4π. From here, the π's cancel out, leaving 36/4 = 9.

         Area of a circle = A = πr²

         R = 1/2d = ½(10) = 5

         A = 5²π = 25π