Equation Of A Quarter Circle

Expanse of a quarter circle is one-fourth part of the whole area of the circle. When a circle is divided into four equal parts, each role is chosen the quarter of a circumvolve. Each quarter is chosen the quadrant of the circle. So, the area of a quarter circle is times of area of the circumvolve.

Quadrants of a circle

What is the area of a quarter circumvolve?

A circle is a geometric figure that traces the path of all those points, which is equidistant to a unique point called the middle of the circumvolve. A quarter of a circle is one-quaternary part of the whole circle. Therefore, the area of a quarter circle is the 4th part of the whole area of a circumvolve.

The formula for the area of a quarter circle using radius

If a circle has a length of radius r, then the area of the circle, A = r²

Then, the expanse of a quarter circle = times of A

= ¼ × πr² = πr²/4

Area of a quarter circle

The formula for the area of a quarter circle using the bore

If the length of the radius is r, then the length of the circle'south diameter, d = 2r, that is, r = d/2.

And so, the expanse of circle = π(d/ii)ⁱⁱ= πdⁱⁱ/4

Area of a quarter circle = ¼ × π(d/ii)² = πdⁱⁱ/16

Surface area of a quarter circumvolve related articles

Circumference of a circle
Circle and its parts
Area of a circle
Quadrants

Solved examples on the surface area of a quarter circle

Instance:

A circle has a radius of 14 cm, find the area of a quarter circle.

Solution:

Radius of circle = 14 cm

Expanse of a quarter circumvolve = πr²/4 = 22/7 × ¼ × 14 × 14 = 154 cm²

Instance:

A circle has a diameter of 32 cm, find the area of a quarter circumvolve.

Solution:

Bore of circle = 32 cm

Expanse of a quarter circle = πd²/sixteen = 22/7 × i/16 × 32ⁱⁱ= 201.14 cm²

Example:

A goat is tied to one corner of a square field. The length of the rope to which the goat is tied is 2m. Find how much area is bachelor for the goat to graze.

Solution:

The grazing field volition exist a quarter of a circumvolve of radius two chiliad.

Area of grazing field = Area of a quarter circle with radius 2 m

= πr²/four = 22/7 × ¼ × 2² = 22/7 ≈ three.14 one thousand²

Video Lessons on Circles

Introduction to Circles

Parts of a Circle

Area of a Circle

All almost Circles

Oft Asked Questions (FAQs)

What is the radius of a quarter of a circle?

The radius of a quarter of a circle is the same as the radius of the given circle.

What is the area of a quadrant?

The area of a quadrant is the same as the surface area of a quarter circle which is πr²/4.

How to find the surface area of a quarter circle when the circumference of the circle is given?

With the value of the circumference of the circumvolve, find the radius of a circumvolve. Then substitute the value of the radius of the circle in the formula of area of a quarter circle using radius which is πr²/iv.

What will be the area of 4 quarter circles?

Together four quarter circles make a whole circle. Therefore, the area of four quarter circles is equal to the area of the circle.