How To Find Area Of Quarter Circle?

How to Find the Area of a Quarter Circle

A circle is a shape that is defined by its center and radius. The area of a circle is equal to r, where is the mathematical constant approximately equal to 3.14 and r is the radius of the circle. A quarter circle is a portion of a circle that is formed by taking one-fourth of the circle’s circumference. The area of a quarter circle is equal to r/4, where r is the radius of the circle.

In this article, we will discuss how to find the area of a quarter circle using both algebraic and graphical methods. We will also provide some examples to help you understand the process.

Algebraic Method

The algebraic method for finding the area of a quarter circle is as follows:

1. Find the radius of the circle.
2. Square the radius.
3. Divide the result by 4.

The following is an example of how to find the area of a quarter circle using the algebraic method:

  • Step 1: The radius of the circle is 5 cm.
  • Step 2: Squaring the radius gives us 5 = 25 cm.
  • Step 3: Dividing the result by 4 gives us 25 cm / 4 = 6.25 cm.

Therefore, the area of the quarter circle is 6.25 cm.

Graphical Method

The graphical method for finding the area of a quarter circle is as follows:

1. Draw a circle with the desired radius.
2. Divide the circle into four equal parts.
3. Find the area of each quadrant.
4. Add the areas of the four quadrants to find the area of the quarter circle.

The following is an example of how to find the area of a quarter circle using the graphical method:

  • Step 1: We draw a circle with a radius of 5 cm.
  • Step 2: We divide the circle into four equal parts.
  • Step 3: The area of each quadrant is equal to r/4, where r is the radius of the circle. In this case, the area of each quadrant is (5 cm)/4 = 6.25 cm.
  • Step 4: We add the areas of the four quadrants to find the area of the quarter circle. In this case, the area of the quarter circle is 6.25 cm + 6.25 cm + 6.25 cm + 6.25 cm = 25 cm.

Therefore, the area of the quarter circle is 25 cm.

Step Formula Explanation
1. Find the radius of the circle. r The radius is the distance from the center of the circle to any point on the circle.
2. Calculate the area of the quarter circle. A = r / 4 The area of a circle is r. To find the area of a quarter circle, you simply divide the area of the entire circle by 4.
3. Round to the nearest tenth. The area of a quarter circle is always a decimal number. You should round your answer to the nearest tenth.

Formula for Area of a Quarter Circle

The area of a quarter circle is equal to one-fourth the area of a full circle. The formula for the area of a circle is r, where is the mathematical constant approximately equal to 3.14 and r is the radius of the circle. So, the formula for the area of a quarter circle is r / 4.

For example, if the radius of a circle is 5 cm, then the area of the quarter circle is (5 cm) / 4 = 19.63 cm.

Steps to Find Area of a Quarter Circle

To find the area of a quarter circle, follow these steps:

1. Measure the radius of the circle.
2. Square the radius.
3. Multiply the result by / 4.

For example, if the radius of a circle is 5 cm, then the area of the quarter circle is (5 cm) / 4 = 19.63 cm.

Additional Tips

  • If you don’t have a ruler to measure the radius of the circle, you can use a string to approximate the radius. Just tie a knot in one end of the string and place the other end at the center of the circle. Then, stretch the string around the circle and measure the length of the string. The length of the string will be approximately equal to the radius of the circle.
  • If you don’t know the value of , you can use the approximate value of 3.14.
  • The area of a quarter circle can also be calculated using the following formula:

A = (1 / 4) * * d

where A is the area of the quarter circle, is the mathematical constant approximately equal to 3.14, and d is the diameter of the circle.

For example, if the diameter of a circle is 10 cm, then the area of the quarter circle is (1 / 4) * * (10 cm) = 78.54 cm.

The area of a quarter circle is equal to one-fourth the area of a full circle. The formula for the area of a quarter circle is r / 4, where is the mathematical constant approximately equal to 3.14 and r is the radius of the circle. To find the area of a quarter circle, follow these steps:

1. Measure the radius of the circle.
2. Square the radius.
3. Multiply the result by / 4.

You can also use the formula A = (1 / 4) * * d to find the area of a quarter circle, where A is the area of the quarter circle, is the mathematical constant approximately equal to 3.14, and d is the diameter of the circle.

3. Examples of Finding Area of a Quarter Circle

Here are some examples of finding the area of a quarter circle:

1. A quarter circle with a radius of 2 cm.

The area of a quarter circle is equal to 1/4 of the area of a full circle. The area of a full circle is r^2, so the area of a quarter circle is r^2 / 4. In this case, the radius is 2 cm, so the area of the quarter circle is (2)^2 / 4 = * 4 / 4 = cm^2.

2. A quarter circle with a diameter of 3 cm.

The diameter of a circle is twice the radius, so the radius of this quarter circle is 3 cm / 2 = 1.5 cm. The area of the quarter circle is r^2 / 4 = (1.5)^2 / 4 = * 2.25 / 4 = 1.31 cm^2.

3. A quarter circle with a circumference of 6 cm.

The circumference of a circle is 2r, so the radius of this quarter circle is 6 cm / 2 = 3 cm / . The area of the quarter circle is r^2 / 4 = (3)^2 / 4 = * 9 / 4 = 2.25 cm^2.

4. A quarter circle with an inscribed square.

An inscribed square is a square that is drawn inside a circle so that all four of its sides touch the circle. The area of a quarter circle with an inscribed square is equal to the area of the square minus the area of the four triangles formed by the intersection of the circle and the square. The area of a square is s^2, where s is the side length. The area of a triangle is 1/2 * b * h, where b is the base and h is the height. In this case, the side length of the square is equal to the diameter of the circle, so s = d = 2r. The height of each triangle is equal to the radius of the circle, so h = r. The area of the square is (2r)^2 = 4r^2. The area of each triangle is 1/2 * 2r * r = r^2. The area of the quarter circle with an inscribed square is 4r^2 – 4r^2 = 0 cm^2.

5. A quarter circle with a circumscribed square.

A circumscribed square is a square that is drawn outside a circle so that all four of its sides touch the circle. The area of a quarter circle with a circumscribed square is equal to the area of the square plus the area of the four triangles formed by the intersection of the circle and the square. The area of a square is s^2, where s is the side length. The area of a triangle is 1/2 * b * h, where b is the base and h is the height. In this case, the side length of the square is equal to the diameter of the circle, so s = d = 2r. The height of each triangle is equal to the radius of the circle, so h = r. The area of the square is (2r)^2 = 4r^2. The area of each triangle is 1/2 * 2r * r = r^2. The area of the quarter circle with a circumscribed square is 4r^2 + 4r^2 = 8r^2 cm^2.

4. Applications of Finding Area of a Quarter Circle

The area of a quarter circle can be used in a variety of applications, such as:

  • Finding the area of a sector of a circle. A sector of a circle is a portion of a circle that is bounded by two radii and an arc. The area of a sector of a circle is equal to the area of a quarter circle multiplied by the fraction of the circle that the sector represents. For example, if a sector of a circle has an angle of 60 degrees, then the area of the sector is equal to 1/4 * r^2 * (60 / 360) = r^2 / 6.
  • Finding the area of a segment of a circle. A segment of a circle is a portion of a circle that is bounded by an arc and a chord. The area of a segment of a circle is equal to the area of

    How to Find Area of Quarter Circle?

The area of a quarter circle can be found using the following formula:

A = r^2 / 4

where:

  • A is the area of the quarter circle
  • is the mathematical constant pi (approximately 3.14159)
  • r is the radius of the circle

For example, if the radius of the circle is 5 cm, then the area of the quarter circle would be:

A = * 5^2 / 4 = 19.635 cm^2

What is the difference between a quarter circle and a semicircle?

A quarter circle is one-fourth of a full circle, while a semicircle is one-half of a full circle. The area of a quarter circle is equal to one-fourth the area of a full circle, while the area of a semicircle is equal to one-half the area of a full circle.

How can I find the area of a quarter circle if I only know the diameter?

If you only know the diameter of a circle, you can find the radius by dividing the diameter by 2. Then, you can use the formula for the area of a quarter circle to find the area.

For example, if the diameter of a circle is 10 cm, then the radius is 10 / 2 = 5 cm. The area of the quarter circle would be:

A = * 5^2 / 4 = 19.635 cm^2

What is the area of a quarter circle with a radius of 1 inch?

The area of a quarter circle with a radius of 1 inch is 0.7854 square inches.

What is the area of a quarter circle with a diameter of 2 feet?

The area of a quarter circle with a diameter of 2 feet is 3.1416 square feet.

we have discussed the different methods for finding the area of a quarter circle. We have seen that the area of a quarter circle can be found using the following formulas:

  • Area = (1/4)r^2
  • Area = (1/2)bh
  • Area = (1/4)d^2

We have also seen how to find the area of a quarter circle using a geometric approach. In this approach, we divide the quarter circle into two right triangles and then use the Pythagorean theorem to find the length of the hypotenuse. We then use the area of a triangle formula to find the area of the quarter circle.

The method you use to find the area of a quarter circle will depend on the information that is given. If you are given the radius of the circle, you can use the formula Area = (1/4)r^2. If you are given the length of the arc of the quarter circle, you can use the formula Area = (1/2)bh. And if you are given the diameter of the circle, you can use the formula Area = (1/4)d^2.

No matter which method you use, the area of a quarter circle can be found easily and quickly.

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