How To Find The Area Of A Quarter Circle
A quadrant is a quarter of a circle. And so to work out the expanse of a quadrant, showtime work out the expanse of the whole circle (use the formula A = π ×r²) and and so divide the respond by 4. Alternatively, you could substitute the radius of the quadrant directly into the formula A = ¼ πr². Allow's take a look at a few examples on working out the area of quadrants:
Example 1
Work out the expanse of this quadrant (radius 8cm).
Method 1 (using the area of a whole circle and dividing by four)
First piece of work out the surface area of the whole circumvolve by substituting the radius of 8cm into the formula for the surface area of the circle:
A = π ×r²
= π ×8²
= 64π (leave the respond as an exact solution as this need to be divided by 4).
And so all you need to do at present is carve up the answer past iv:
Area of a quadrant = 64π ÷four = 16π = 50.three cm² to 3 significant figures.
Method 2 (using ¼ πr²)
Substitute r = 8 directly into the formula A = ¼ πr².
A = ¼ πr².
A = ¼ × π × 8².
A = fifty.3 cm²
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As you can run into information technology gives exactly the aforementioned reply as method 1.
Example 2
Work out the area of this quadrant (radius 3.8m).
Like example i, brainstorm by substituting the radius of iii.8m into the formula for the expanse of the circle:
A = π ×r²
= π ×3.eight²
= 14.44π (leave the respond as an exact solution every bit this need to be divided by 4).
Over again, all y'all need to practise now is separate the answer by iv:
Expanse of a quadrant = 14.44π ÷4 = 16π = eleven.iii m² to 3 significant figures.
Method two
Substitute r = 3.8m directly into the formula A = ¼ πr².
A = ¼ πr².
A = ¼ × π × 3.eight².
A = 11.3 chiliad²
Equally you lot can run into it gives exactly the same reply equally method ane.
Questions & Answers
Question: Can you find the area of quadrant of a circle whose circumference is 22?
Reply: Beginning, detect the radius of the circle past dividing the circumfernece by Pi and halving the answer to give 3.501 to three decimal places.
Now use 0.25*Pi*radius^ii to give the surface area of the quadrant 0.25*Pi*three.501^two = 9.63 to 2 decimal places.
Question: If the area of a circle is 100 cm2, what's the surface area of one of its quadrants?
Reply: All you need to practice is carve up 100 by 4 to give 25 cm^2.
Question: Is the surface area of a quarter-circle supposed to be (8² x π) /4 ?
Respond: Aye, the formula tin exist written equally (radius² ten π) /iv.
I think you are showing an instance when the radius of the quarter circumvolve is viii.
Question: What is the expanse of a quadrant with a radius of 6cm, given in terms of Pi?
Answer: First square the radius of 6 to give 36.
Now multiply 36 by Pi to give 36Pi
Adjacent, split up the respond past 4 to 9Pi.
Question: What is the formula for working out the area of a quadrant?
Reply: 0.25*Pi*r^2.
Question: If the wheel of a gate is 3 anxiety from the wall and it turns over 90 degrees, what is the distance covered past the wheel?
Answer: First double 3 feet to give a bore of 6 anxiety.
Side by side multiply 3.14 by 6 to give the circumference of the whole circle which is xviii.84 feet.
Now divide the answer by four equally xc degrees is 1/4 of the whole circle to give four.7 feet to 1 decimal place.
Question: Can you discover the area of a quadrant whose radius is 9cm?
Answer: Square ix to requite 81.
Now multiply 81 by 3.14 to give 254.34.
Finally divide 254.34 by 4 to requite 63.half-dozen to one decimal identify.
Question: What is the area of the quadrant with a radius of 14cm ?
Answer: The area of the whole circle is Pi times 14 times xiv which gives 615.75... cm^two.
Now carve up this answer past four to give 153.nine cm^2 to 1 decimal identify (or 49Pi).
Question: What is the surface area of a quadrant with a radius of 4.3cm?
Answer: Work out 0.25 mutlplied by Pi multiplied past 4.3^2 to requite xiv.5 cm^2 rounded to one decimal place.
Question: What is the Area for 1/4 circle with radius of six?
Answer: First square the radius to requite 36, and multiply it by π to requite 36π.
Now divide this respond by iv to give 9π.
Question: The radius of a quarter circle is iii millimeters. What is the quarter circle's area? (r=3 mm, Pi = 3.fourteen)
Answer: Work out iii^2 which is ix.
Now times 9 by 3.14 which is 28.26.
At present split up 28.26 by 4 to requite seven.065 mm^ii.
d,annalee on September 08, 2013:
Non what i was looking for but good
Source: https://owlcation.com/stem/Area-of-a-quadrant-a-quarter-of-a-circle-Finding-the-area-of-quadrants
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