Before understanding what is the area the a 4 minutes 1 circle, let united state recall what is a circle and a quarter circle. A circle is a locus (collection) of point out that are at a resolved distance indigenous a addressed point. This fixed suggest and the resolved distance are called the "center" and "radius" respectively. A quarter-circle is one-fourth section of a circle. Therefore the area the a 4 minutes 1 circle is exactly one-fourth the the area that the full circle.
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Let us learn the formula for the area of a circle along with its proof, a few solved examples, and practice questions.
| 1. | What is a quarter Circle (Quadrant)? |
| 2. | Area of a 4 minutes 1 Circle Formulas |
| 3. | How to find the Area of a 4 minutes 1 Circle? |
| 4. | FAQs onArea of a 4 minutes 1 Circle |
What Is a 4 minutes 1 Circle (Quadrant)?
The area (or) portion that is developed by 2 radii that are perpendicular to each other and one-fourthportion of the one of a circle is recognized as a quarter circle. This is likewise known together a quadrant of a circle. I.e., if we divide a circle into 4 same parts, each part is a 4 minutes 1 circle (or) a quadrant.
Area the a 4 minutes 1 Circle Formulas
Consider a circle of radius 'r' and diameter 'd'. We understand that d = 2r. Let us derive the formulas because that the area of a quarter circle in terms of radius and also diameter.
Area the a 4 minutes 1 Circle making use of Radius
We recognize that the area that a circle isπr2. Together we learned currently in the previous section, a quarter circle is one-fourth part of a full circle and also thus that is area is one-fourth the the area the the circle.
Thus, the area of a quarter circle in regards to radius =πr2/ 4
Area the a quarter Circle using Diameter
Since d = 2r, we have actually r = d/2. Substituting this in the over formula, we can obtain the area of a 4 minutes 1 circle in terms of diameter.
The area of a quarter circle =π(d/2)2/ 4 =πd2/ 16
Thus,the area that a 4 minutes 1 circle in terms of diameter =πd2 / 16
Note:Here,π is a mathematical continuous whose worth is considered to it is in 22 / 7 (or)3.141592...
How to find the Area of a quarter Circle?
Consider a one of radius 'r'. Here are the procedures to discover the area that thequarter circle.
If the radius (r) is offered then straight away instead of it in the formulaπr2/ 4.If the diameter (d) is offered then either deal with d = 2r because that 'r'and use the formulaπr2/ 4 (or) right away substitute the worth of d in the formulaπd2 / 16.If the circumference (C) is offered then solve C = 2πr for 'r' and also substitute the in the formulaπr2/ 4.If area(A) is provided then either fix A =πr2for 'r'and substitute it in the formulaπr2/ 4 (or) simply discover A / 4.Now that we have interpreted the formula ad technique to discover area the a quarter circle, permit us have actually a look at a few solved examples for far better understanding.
Solved examples on Area that a 4 minutes 1 Circle
Example 1:The radius that a one park is 40 yards. A quarter circular portion of this part is allotted for play equipment. Find the area that the section that is allotted because that the playing equipment. Useπ = 3.142.
Solution:
The radius that the circular park is, r = 40 yards.
The area of the section allotted for playing equipment can be discovered by utilizing the area that a quarter circle formula.
The section of the park allotted because that playing equipment =πr2/ 4 =(3.142)(40)2/ 4 =1256.8 square yards.
Answer: The required area that playing equipment =1256.8 square yards.
Example 2:James ordered a pizza for him and his 3 friends. They desire to share that equally. The pizza is circular shaped and its diameter is 16 inches. Utilizing the area of a 4 minutes 1 circle formula, uncover the lot of pizza that each of them got. Useπ = 3.14.
Solution:
The diameter the the provided pizza is, d = 16inches.
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Since the pizza is separated into 4 same parts, each part is a 4 minutes 1 circle and also hence the area have the right to befound by using the area of a 4 minutes 1 circle formula.