Area Of A Quater Circle

Marker, a math enthusiast, loves writing tutorials for stumped students and those who demand to brush up on their math skills.

Read on to learn how to find the area of a quadrant! — Read on to learn how to notice the area of a quadrant!

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What Is a Quadrant?

A quadrant is a quarter of a circle. So to work out the area of a quadrant, first work out the area of the whole circle (utilise the formula A = π ×r²) and and then dissever the answer by 4. Alternatively, you could substitute the radius of the quadrant direct into the formula A = ¼ πr². Let'due south accept a look at a few examples on working out the area of quadrants:

Example i

Work out the expanse of this quadrant (radius 8cm).

area-of-a-quadrant-a-quarter-of-a-circle-finding-the-area-of-quadrants

Method one (using the area of a whole circle and dividing by iv)

First work out the area of the whole circle past substituting the radius of 8cm into the formula for the surface area of the circle:

A = π ×r²

= π ×8²

= 64π (leave the answer as an exact solution as this need to be divided by 4).

So all you need to practise now is separate the answer 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.

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Questions & Answers

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

Reply: All you need to do is divide 100 by 4 to requite 25 cm^two.

Question: Can you discover the expanse of quadrant of a circle whose circumference is 22?

Respond: First, find the radius of the circle by dividing the circumfernece by Pi and halving the answer to give 3.501 to iii decimal places.

Now use 0.25*Pi*radius^ii to requite the surface area of the quadrant 0.25*Pi*3.501^two = ix.63 to two decimal places.

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

Answer: First foursquare the radius of vi to requite 36.

At present multiply 36 by Pi to give 36Pi

Next, divide the answer by four to 9Pi.

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

Answer: 0.25*Pi*r^2.

Question: Is the area of a quarter-circle supposed to exist (8² 10 π) /iv ?

Answer: Yes, the formula can be written equally (radius² x π) /4.

I recollect you are showing an example when the radius of the quarter circle is 8.

Question: If the bike of a gate is three anxiety from the wall and information technology turns over 90 degrees, what is the distance covered past the wheel?

Respond: Commencement double 3 feet to give a bore of 6 feet.

Next multiply three.14 by 6 to requite the circumference of the whole circle which is 18.84 feet.

Now divide the reply by 4 as 90 degrees is 1/four of the whole circle to requite 4.vii feet to 1 decimal place.

Question: Tin yous 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 1 decimal place.

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

Reply: The area of the whole circle is Pi times 14 times 14 which gives 615.75... cm^2.

At present split up this respond by 4 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 four.3cm?

Respond: Work out 0.25 mutlplied by Pi multiplied past 4.three^2 to give 14.5 cm^2 rounded to ane decimal place.

Question: What is the Area for one/4 circle with radius of vi?

Answer: Start foursquare the radius to give 36, and multiply it by π to give 36π.

Now divide this respond by iv to requite 9π.

Question: The radius of a quarter circle is 3 millimeters. What is the quarter circle's area? (r=3 mm, Pi = three.14)

Answer: Piece of work out iii^ii which is 9.

Now times 9 by 3.xiv which is 28.26.

Now split up 28.26 by 4 to give 7.065 mm^two.

d,annalee on September 08, 2013:

Not what i was looking for but good