Many Ways To Find The Area Of A Circle by mathworksheets

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Many Ways To Find The Area Of A Circle

<html>
<p>There are multiple ways to find the area of a given circle. The area of the circle is the number of square units inside its boundaries. So, if we can count number of square units inside the circle boundary then we can tell the area of this circle as explained in the image below:</p>
<p><br></p>
<p><img src="http://areacircle.com/area_of_a_circle_basic.png"/></p>
<p><br></p>
<p>But the problem with the above method is that not all the squares are fully inside the circle's boundary, look near the circle boundary there are many squares which are partially inside the circle and partially outside of it. Hence, using the above method we can't find the exact value of the area of a given circle. So we need to find some other method to find its area.</p>
<p><br></p>
<p>Mathematicians kept on working to find a new and easy way to find the area of a circle. Finally they found another easier way, which is to cut the circle into pieces (same way as we cut the pizza into slices) and then arrange these slices in such a way that it forms a rectangle. Wow, once we convert the circle into a rectangle then its very easy to find the area of this rectangle as it is length times it width and hence the area of the circle. This method is explained below and using this method the formula to find the area of a circle was invented. Consider a circle with radius "r"</p>
<p><br></p>
<p>http://4.bp.blogspot.com/-vvZ4c_V7cq4/Tyyv62HXj9I/AAAAAAAAAB0/ASragoYNO-U/s1600/circle.png</p>
<p><br></p>
<p>Now slice this circle into two semi-circles as shown in next image:</p>
<p>http://4.bp.blogspot.com/-in4HrOrmf8Y/Tyy6lfpDHFI/AAAAAAAAAB8/4ix4Eh4Jn_Y/s1600/sliced-circle.png</p>
<p><br></p>
<p>Now get these 16 slices and color them red and green and arrange them such way to make a rectangle as shown in the next image:</p>
<p>http://2.bp.blogspot.com/-yTC0G3lLE5U/TyzNpozFsEI/AAAAAAAAACE/H6UahcYLJ00/s1600/Area-of-a-circle-formula.png</p>
<p>Hence the formula to find the area of a circle was developed and we can always use this formula to find the area of circle when its radius is given.</p>
<p><br></p>
<p>http://areacircle.com/Area_of_a_circle_from_radius_1.png</p>
<p><br></p>
<p>2ndly when the diameter of a circle is given then we can divide it by 2 to find its radius and same formula is used to find the area of the given circle.</p>
<p>http://areacircle.com/Area_of_a_circle_from_diameter_1.png</p>
<p><br></p>
<p>But sometimes we are given with the circumference of the circle and still we can find the area of this circle. The first step is to find the radius of the circle from its circumference and then use the radius in the above area formula to find the area of the circle. Use the following practice sheet to learn how find the area of a circle when its circumference is given:</p>
<p><a href="http://areacircle.com/Area%20of%20a%20circle%20from%20circumference.pdf">Area of a circle when its circumference is given</a></p>
<p>Above presentation is useful for grade 6 to 8 students.</p>
</html>

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@giantbear · Feb 28 '17

Wow, I have never thought of adding any worksheets I create here on Steemit.  Good job @mathworksheets I am following you now.  Are you a teacher?  I have been a teacher for 22 years now, and all my students signed up for Steemit.  Glad I saw this post!

👍 mathworksheets

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@mathworksheets · Feb 28 '17

Dear giantbear, I am a tutor in math and physics. I tutor math and science to students from grade 1 to 12 since 1995. Professionally I am accountant and have own small accounting firm here in Vancouver BC (that's for earn my bread and butter). But from my blood I am a math teacher and I taught upto grade 12 back in India for 7 years before migrating to Canada.
I really appreciate your kind words and encourage you to post your lesson plans and worksheets here on steemit too, it is very rewarding along with sharing your knowledge and skills with the community.
God Bless
Manjit

👍 giantbear

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@giantbear · Feb 28 '17

Very interesting.  This is really a great idea.  All my students signed up for Steemit so perhaps they can learn from here.  LOL!  You sound exactly like a Math teacher.  I teach Maths too and I love it!

👍 mathworksheets

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1 reply

@pompe72 · Feb 27 '17

If you bend space and make the circle a square, you can just multipy the sides.

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@mathworksheets · Feb 28 '17

Awesome idea ! This way you can find the area of any irregular two dimensional shape by bending it into a square and find side x side to find its area.

👍 pompe72

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@pompe72 · Feb 28 '17

Awesome idea, but it doesn't even get an upvote and that's why steemit sucks.

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1 reply