A quadrant is a 4 minutes 1 of a circle. Therefore to occupational out the area of a quadrant, first work out the area that the whole circle (use the formula A = π ×r²) and also then division the prize by 4. Alternatively, you can substitute the radius of the quadrant directly into the formula A = ¼ πr². Let’s take a look at a few examples on functioning out the area of quadrants:

Example 1

Work the end the area that this quadrant (radius 8cm).

You are watching: Area of a quarter circle formula


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Method 1 (using the area of a entirety circle and dividing through 4)

First work-related out the area of the totality circle by substituting the radius of 8cm right into the formula for the area that the circle:

A = π ×r²

= π ×8²

= 64π (leave the prize as precise solution as this need to be split by 4).

So every you must do now is division the answer by 4:

Area of a quadrant = 64π ÷4 = 16π = 50.3 cm² come 3 significant figures.

Method 2 (using ¼ πr²)

Substitute r = 8 straight into the formula A = ¼ πr².

A = ¼ πr².

A = ¼ × π × 8².


A = 50.3 cm²


As you have the right to see that gives precisely the same answer as method 1.

Example 2

Work the end the area that this quadrant (radius 3.8m).


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Like instance 1, begin by substituting the radius the 3.8m right into the formula because that the area of the circle:

A = π ×r²

= π ×3.8²

= 14.44π (leave the price as an exact solution together this should be divided by 4).


Again, every you should do now is division the price by 4:

Area that a quadrant = 14.44π ÷4 = 16π = 11.3 m² to 3 significant figures.

Method 2

Substitute r = 3.8m directly into the formula A = ¼ πr².

A = ¼ πr².

A = ¼ × π × 3.8².

A = 11.3 m²

As you deserve to see that gives exactly the exact same answer as method 1.

Questions & Answers

Question: have the right to you find the area the quadrant of a circle whose circumference is 22?

Answer: First, find the radius of the circle by dividing the circumfernece by Pi and halving the answer to offer 3.501 to 3 decimal places.

Now use 0.25*Pi*radius^2 to give the area that the quadrant 0.25*Pi*3.501^2 = 9.63 come 2 decimal places.


Question: If the area that a circle is 100 cm2, what's the area of among its quadrants?

Answer: all you need to do is divide 100 through 4 to provide 25 cm^2.

Question: What is the area of a quadrant through a radius that 6cm, offered in terms of Pi?


Answer: an initial square the radius that 6 to give 36.

Now main point 36 through Pi to offer 36Pi

Next, division the price by 4 to 9Pi.

Question: What is the formula for functioning out the area of a quadrant?

Answer: 0.25*Pi*r^2.

Question: Is the area of a quarter-circle an alleged to it is in (8² x π) /4 ?

Answer: Yes, the formula have the right to be composed as (radius² x π) /4.

I think you are showing an example when the radius of the 4 minutes 1 circle is 8.

Question: If the wheel that a gate is 3 feet indigenous the wall surface and it transforms over 90 degrees, what is the distance extended by the wheel?

Answer: First twin 3 feet to offer a diameter that 6 feet.

Next multiply 3.14 by 6 to offer the circumference of the whole circle which is 18.84 feet.

Now divide the prize by 4 together 90 degrees is 1/4 that the entirety circle to give 4.7 feet come 1 decimal place.

Question: deserve to you discover the area that a quadrant who radius is 9cm?


Answer: Square 9 to offer 81.

Now multiply 81 through 3.14 to provide 254.34.


Finally division 254.34 by 4 to offer 63.6 come 1 decimal place.

Question: What is the area of the quadrant with a radius the 14cm ?

Answer: The area the the totality circle is Pi time 14 times 14 which gives 615.75... Cm^2.

Now division this answer by 4 to give 153.9 cm^2 to 1 decimal location (or 49Pi).

Question: What is the area the a quadrant through a radius the 4.3cm?

Answer: occupational out 0.25 mutlplied by Pi multiplied by 4.3^2 to provide 14.5 cm^2 rounded to 1 decimal place.

Question: What is the Area for 1/4 circle through radius that 6?

Answer: an initial square the radius to give 36, and also multiply the by π to give 36π.

Now division this prize by 4 to give 9π.

Question: The radius that a quarter circle is 3 millimeters. What is the 4 minutes 1 circle's area? (r=3 mm, Pi = 3.14)

Answer: work-related out 3^2 i beg your pardon is 9.

Now times 9 through 3.14 i beg your pardon is 28.26.


Now divide 28.26 through 4 to give 7.065 mm^2.

See more: What Does It Mean By Employer Name On An Application? What Does Employer Name Mean

Comments

d,annalee on September 08, 2013:

Not what ns was looking for but good


By
Mark
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