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Find the circumference of a circular disk whose area is 100pi square centimeters.

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eyad69 | Student, Undergraduate | eNoter

Posted November 26, 2010 at 3:09 AM via web

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Find the circumference of a circular disk whose area is 100pi square centimeters.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted November 26, 2010 at 3:10 AM (Answer #1)

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Given that the area of the circle is A = 100pi cm^2.

We know that the area of the circle IS :

A = r^2 * pi = 100*pi

==> Divide by pi:

==> r^2 = 100

==> r= 10

Now we will find the circumference:

==> C = 2*pi *r

 ==> C = 2*pi* 10 = 20*pi

==> Then the circumference of the circle is = 20*pi

The area = 20*pi

We know that the formula for the area of a circle is:

 A = r^2 *pi where r is the radius:

==> r^2 * pi = 100*pi

Now we will divide by pi:

==> r^2 = 100

==> r= 10

Now we will calculate the circumference:

 We know that:

C = 2*pi*r

==> C= 2*10* pi

            = 20*pi

Also we could write pi = 22/7

==> C = 20*22/7 = 62.89 cm


 
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changchengliang | Elementary School Teacher | (Level 2) Adjunct Educator

Posted November 26, 2010 at 3:29 AM (Answer #2)

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The task is to

Find the circumference of a circular disk whose area is 100pi square centimeters.

The area of circle is given by the formula:

A = pi * r ^2

Substitute the given value of A into the formula, we get:

100 pi = pi * r^2

Divide by pi on both sides:

100 = r^2

10^2 = r^2

It follows that

r=10

Circumference of circle is given by the formula C=2*pi*r

C = 2 * pi * 10

20*pi

The required answer: circumference of the disk is 20*pi cm

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neela | High School Teacher | Valedictorian

Posted November 26, 2010 at 5:09 AM (Answer #3)

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The area of a circular disk with radius r is given by pi*r^2, wher pi  is the ratio of the circumference to the diameter of the circle.

The actual area of the disk is 100pi sq cm

Therefore pr^2 = 100pi sq cm

Therefore r ^2 = 100 sq cm. So r = sqrt100 = 10 cm.

So the radius of the disk is 10 cm.

The circumference c of the circular disk is given by:

c = 2pir.

Therefore c = 2p*10 cm = 20pi.

Therefore the circumference of the disk = 20 pi.

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