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.

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.

Circles have an area of πr_2, where r is the radius. If this circle has an area of 144_π, then you can solve for the radius:

πr_2 = 144_π

r 2 = 144

r =12

When the groundskeeper goes from the center of the circle to the edge, he's creating a radius, which is 12 meters.

When he travels ¼ of the way around the circle, he's traveling ¼ of the circle's circumference. A circumference is 2_πr_. For this circle, that's 24_π_ meters. One-fourth of that is 6_π_ meters.

Finally, when he goes back to the center, he's creating another radius, which is 12 meters.

In all, that's 12 meters + 6_π_ meters + 12 meters, for a total of 24 + 6_π_ meters.

The formula for the area of a circle is A = _πr_2.

We are given the area, and by substitution we know that 13_π_ = _πr_2.

We divide out the π and are left with 13 = _r_2.

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

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

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

Circles have an area of πr_2, where r is the radius. If this circle has an area of 144_π, then you can solve for the radius:

πr_2 = 144_π

r 2 = 144

r =12

When the groundskeeper goes from the center of the circle to the edge, he's creating a radius, which is 12 meters.

When he travels ¼ of the way around the circle, he's traveling ¼ of the circle's circumference. A circumference is 2_πr_. For this circle, that's 24_π_ meters. One-fourth of that is 6_π_ meters.

Finally, when he goes back to the center, he's creating another radius, which is 12 meters.

In all, that's 12 meters + 6_π_ meters + 12 meters, for a total of 24 + 6_π_ meters.

The formula for the area of a circle is A = _πr_2.

We are given the area, and by substitution we know that 13_π_ = _πr_2.

We divide out the π and are left with 13 = _r_2.

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

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

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

The area of an annulus is

where is the radius of the larger circle, and is the radius of the smaller circle.

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.