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Find the ratio of the areas of two circles whose radii are 4 cm and 7 cm.

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arman7763 | (Level 2) Honors

Posted January 7, 2010 at 9:37 PM via web

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Find the ratio of the areas of two circles whose radii are 4 cm and 7 cm.

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krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted January 7, 2010 at 10:07 PM (Answer #1)

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The area of a circle is directly given by the formula pi*(radius)^2. Thus the area of a circle is directly proportional to square of its radius.

Therefore ratio of areas of two circles with radii r1 and r2 will be equal to ratio of (r1)^2 and (r2)^2.

In the question it is given:

r1 = 4 cm and r2 = 7 cm.

Therefore ration of areas of these two circles is:

[(r1)^2]/[(r2)^2] = (4^2)/(7^2) = 16/49 = 0.32653

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neela | High School Teacher | (Level 3) Valedictorian

Posted January 7, 2010 at 10:19 PM (Answer #2)

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A circles area is pi times the square of its radius or area A of the circle is given by:

A = pi*r^2

So,if the radii of the two circles are a and b, then their areas are pi*a^2 and pi*b^2, where pi is a constant = circumference/(2*radius). So, the circles'  areas  with radius a and b, are in the ratio, pi*a^2 : pi*b^2 = a^2 : b^2.

Here, a = 4cm and b=7^cm. Therefore, the circles' areas are in the ratio,  (4cm)^2  : (7cm)^2  or  in the ratio 16:49

 

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