Area Of Quarter Circle Formula

Area of a Quarter Circle

Before knowing what is the expanse of a quarter circumvolve, let us remember what is a circumvolve and a quarter circle. A circle is a locus (collection) of points that are at a fixed distance from a stock-still point. This stock-still point and the fixed distance are called the "eye" and "radius" respectively. A quarter-circle is one-fourth portion of a circle. And so the area of a quarter circle is exactly ane-4th of the area of the full circle.

Let us larn the formula for the area of a circumvolve along with its proof, a few solved examples, and do questions.

1.	What is a Quarter Circle (Quadrant)?
2.	Area of a Quarter Circle Formulas
3.	How to Find the Surface area of a Quarter Circumvolve?
four.	FAQs on Area of a Quarter Circumvolve

What Is a Quarter Circle (Quadrant)?

The area (or) portion that is formed by two radii that are perpendicular to each other and one-fourth portion of the circumference of a circle is known as a quarter circle. This is as well known as a quadrant of a circle. i.e., if nosotros carve up a circle into 4 equal parts, each part is a quarter circle (or) a quadrant.

Surface area of a Quarter Circle Formulas

Consider a circle of radius 'r' and diameter 'd'. We know that d = 2r. Allow us derive the formulas for the area of a quarter circle in terms of radius and diameter.

Surface area of a Quarter Circumvolve Using Radius

We know that the area of a circle is πr². Every bit we learned already in the previous department, a quarter circle is one-fourth portion of a full circle and thus its area is 1-fourth of the expanse of the circle.

Thus, the area of a quarter circumvolve in terms of radius = πrⁱⁱ / 4

Area of a Quarter Circle Using Diameter

Since d = 2r, nosotros accept r = d/2. Substituting this in the higher up formula, we can get the area of a quarter circumvolve in terms of diameter.

The area of a quarter circle = π(d/two)² / 4 = πd^two / 16

Thus, the area of a quarter circumvolve in terms of bore = πd² / 16

Note: Hither, π is a mathematical constant whose value is considered to be 22 / 7 (or) iii.141592...

Area of a quarter circle (or quadrant) is pi r squared by 4 or pi d squared by 16

How to Find the Expanse of a Quarter Circumvolve?

Consider a circumvolve of radius 'r'. Here are the steps to notice the expanse of the quarter circle.

If the radius (r) is given then directly away substitute it in the formula πr² / iv.
If the diameter (d) is given then either solve d = 2r for 'r' and use the formula πr² / 4 (or) straight away substitute the value of d in the formula πd² / 16.
If the circumference (C) is given then solve C = 2πr for 'r' and substitute it in the formula πr² / 4.
If area(A) is given then either solve A = πr² for 'r' and substitute it in the formula πr² / 4 (or) simply detect A / four.

Now that we take understood the formula and method to find the surface area of a quarter circle, let us have a look at a few solved examples for improve understanding.

Examples on Surface area of a Quarter Circle

Example 1: The radius of a circular park is 40 yards. A quarter round portion of this part is allotted for playing equipment. Discover the expanse of the portion that is allotted for the playing equipment. Utilise π = three.142.

Solution:

The radius of the round park, r = 40 yards.

The expanse of the portion allotted for playing equipment can be institute by using the area of a quarter circumvolve formula.

The portion of the park allotted for playing equipment = πrⁱⁱ / four = (3.142)(40)² / 4 = 1256.8 foursquare yards.

Respond: The required area of playing equipment = 1256.8 foursquare yards.
Case ii: James ordered a pizza for him and his three friends. They want to share it equally. The pizza is circular shaped and its diameter is 16 inches. Using the surface area of a quarter circumvolve formula, discover the corporeality of pizza that each of them got. Utilise π = 3.14.

Solution:

The diameter of the given pizza is, d = sixteen inches.

Since the pizza is divided into 4 equal parts, each part is a quarter circumvolve and hence its surface area can be plant by using the area of a quarter circle formula.

Method 1

The radius of the pizza is, r = d/ii = 16/2 = 8 inches.

Area of each portion = πr² / 4 = (iii.14)(8)² / iv = 50.24 square inches.

Method 2

Area of each portion = πd^two / 16 = (3.14)(16)² / sixteen = l.24 square inches.

Answer: The area of each portion of pizza = 50.24 square inches.

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Practice Questions on Expanse of a Quarter Circle

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FAQs on Surface area of a Quarter Circle

What Is a Quarter of a Circle Called?

When a circle is divided into iv equal parts, iv quarters are formed and each of these quarters is known as a "quadrant".

What Is the Area of a Quarter Circle?

The surface area of a quarter circle is one-fourth of the area of a full circle of radius 'r'. i.e., the area of the quarter circle = πr² / iv.

How To Calculate the Area of a Quarter Circle?

If r, d, C, and A are the radius, diameter, circumference, and area of a circle, ane of these pieces of information is sufficient to observe the expanse of a quarter circumvolve as explained beneath.

If r is given use the formula πrⁱⁱ / four.
If d is given apply the formula πd^two / 16.
If C is given, then solve C = 2πr for 'r' and use the formula πrⁱⁱ / 4.
If A is given, then find A / four.

What Is the Area of a Quarter Circle in Terms of Radius?

Consider a circumvolve of radius 'r'. Then the area of a quarter circumvolve in terms of r is πrⁱⁱ / 4.

How To Find the Area of a Quarter Circle Using the Diameter?

If r and d are the radius and the diameter of a circle, then nosotros know that d = 2r. If the value of 'd' is given, then we can find the area of a quarter circle in i of the following ways:

Notice 'r' using r = d/ii then use the formula πrⁱⁱ / iv (or)
Straight abroad substitute the value of d in the formula πd² / 16.

What Is the Area of Quadrant of a Circle?

The area of a quadrant of a circumvolve is nothing just the area of a quarter circumvolve and hence it is one-fourth of the area of a full circle. i.e., if 'r' is the radius of a full circumvolve, then the area of quadrant of a circle = πr² / 4.

What Is the Formula for Perimeter of a Quarter Circumvolve?

A quarter-circle is fabricated up of two radii and ane-4th portion of the circumference of a circle. So the perimeter of a quarter circle of radius 'r' is, r + r + (2πr)/iv = 2r + πr/2.