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.
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
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.
Equation Of A Quarter Circle,
Source: https://byjus.com/maths/area-of-a-quarter-circle/#:~:text=The%20area%20of%20a%20quadrant%20is%20the%20same%20as%20the,which%20is%20%CF%80r2%2F4.
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