Radius - ACT Math

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 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

Explanation: Visualizing the rectangle inside the circle (corners touching the circumference of the circle and the center of the rectangle is the center of the circle) you will see that the rectangle can be divided into 8 congruent right triangles, with the hypotenuse as the radius of the circle. Calculating the radius you divide each side of the rectangle by two for the sides of each right triangle (giving 6 and 8). The hypotenuse (by pythagorean theorem or just knowing right triangle sets) the hypotenuse is give as 10. Area of a circle is given by πr2. 102 is 100, so 100π is the area.

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.

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

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

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

Find the total area of the circle, then use the area formula to find the radius.

Area of section A = section B = section C

Area of circle X = A + B + C = 12π+ 12π + 12π = 36π

Area of circle = where r is the radius of the circle

36π = πr2

36 = r2

√36 = r

6 = r

To Find your answer, we would use the formula: C=2πr. We are given that C = 29.5. Thus we can plug in to get \[29.5\]=2πr and then multiply 2π to get 29.5=(6.28)r. Lastly, we divide both sides by 6.28 to get 4.70=r. (The information given of 22 ounces is useless)

For the circle to be tangent to the y-axis, it must have its outer edge on the axis. The center is 8 units from the edge.

We know that the formula for the area of a circle is πr_2. Therefore, we must set 49_π equal to this formula to solve for the radius of the circle.

49_π_ = _πr_2

49 = _r_2

7 = r

Plug the radius into the circumference formula:

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_.

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 = 10_π_.

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

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.

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.

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 .