A quadrant is a 4 minutes 1 of a circle. For this reason to job-related out the area the a quadrant, very first work out the area that the whole circle (use the formula A = π ×r²) and also then division the answer by 4. Alternatively, you can substitute the radius of the quadrant directly into the formula A = ¼ πr². Let’s take it a look in ~ a few examples on functioning out the area the quadrants:

Example 1

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

You are watching: How do you find the area of a quarter circle


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

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

A = π ×r²

= π ×8²

= 64π (leave the answer as specific solution together this should be split by 4).


So every you need to do currently is divide the prize by 4:

Area of a quadrant = 64π ÷4 = 16π = 50.3 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 = 50.3 cm²

As you can see the gives specifically the exact same answer as technique 1.

Example 2

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


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Like example 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 answer as an accurate solution together this need to be split by 4).

Again, every you need to do currently is divide the answer by 4:

Area of a quadrant = 14.44π ÷4 = 16π = 11.3 m² to 3 far-ranging 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 can see it gives specifically the same answer as method 1.

Questions & Answers

Question: deserve to you discover the area the quadrant that a circle who circumference is 22?


Answer: First, discover the radius of the circle by separating the circumfernece by Pi and halving the price to provide 3.501 to 3 decimal places.

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

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

Answer: every you have to do is divide 100 by 4 to give 25 cm^2.

Question: What is the area of a quadrant with a radius of 6cm, provided in terms of Pi?

Answer: an initial square the radius the 6 to provide 36.

Now multiply 36 by Pi to provide 36Pi

Next, divide the price by 4 come 9Pi.

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


Answer: 0.25*Pi*r^2.

Question: Is the area of a quarter-circle claimed to be (8² x π) /4 ?

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

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


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

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

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

Now division the prize by 4 as 90 levels is 1/4 that the totality circle to offer 4.7 feet to 1 decimal place.

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

Answer: Square 9 to provide 81.

Now main point 81 by 3.14 to provide 254.34.

Finally division 254.34 by 4 to give 63.6 to 1 decimal place.

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

Answer: The area of the whole circle is Pi times 14 time 14 which offers 615.75... Cm^2.

Now divide this price by 4 to give 153.9 cm^2 come 1 decimal ar (or 49Pi).

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

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


Question: What is the Area for 1/4 circle v radius of 6?

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

Now division this prize by 4 to provide 9π.

Question: The radius of a 4 minutes 1 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 time 9 through 3.14 i m sorry is 28.26.

Now division 28.26 by 4 to offer 7.065 mm^2.

See more: How To Disband Guild In Wow Guild? How To Disband A Guild : R/Wow

Comments

d,annalee ~ above September 08, 2013:

Not what i was spring for but good


By
Mark
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