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Area of Circle - Pre-Algrebra

by LAURA
(KANSAS)










































There are to concentric circles on the playground. The diameter of the larger circle is 40% greater than the diameter of the smaller circle. The area of the larger circle is what percent greater than the area of the smaller circle.

Comments for Area of Circle - Pre-Algrebra

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Apr 22, 2012
Ratio of Areas - Circle
by: Staff

Question:

by LAURA
(KANSAS)

There are to concentric circles on the playground. The diameter of the larger circle is 40% greater than the diameter of the smaller circle. The area of the larger circle is what percent greater than the area of the smaller circle.


Answer:

r = radius of the small circle

d = diameter of the small circle

r = d/2


Area of the small circle = πr²

Area of the small circle = π(d/2)²

Area of the small circle = πd²/4


diameter of the large circle = diameter of the small circle + 40% of the diameter of the small circle

diameter of the large circle = d + 40% * d

diameter of the large circle = d + 0.4 * d

diameter of the large circle = (1 + 0.4) * d

diameter of the large circle = (1.4) * d

diameter of the large circle = 1.4d



Area of the large circle = π(1.4d)²/4


Area of the large circle : Area of the small circle = [π(1.4d)²/4] : (πd²/4)


(Area Large Circle)/(Area Small Circle) = [π(1.4d)²/4] / (πd²/4)

(Area Large Circle)/(Area Small Circle) = [π(1.4d)²/4] * (4/πd²)

(Area Large Circle)/(Area Small Circle) = [(π*1.4²*d²)/4] * (4/πd²)

(Area Large Circle)/(Area Small Circle) = (1.4²)*[(π*d²)/4] * (4/πd²)

(Area Large Circle)/(Area Small Circle) = (1.4²)*[(πd²)/4] * (4/πd²)

(Area Large Circle)/(Area Small Circle) = (1.4²)*[(πd²)/(πd²)] * [(4/4)]

(Area Large Circle)/(Area Small Circle) = (1.4²)*1*1

(Area Large Circle)/(Area Small Circle) = (1.4²)

(Area Large Circle)/(Area Small Circle) = 1.4²

(Area Large Circle)/(Area Small Circle) = 1.96


% increase in size = (1.96 - 1)*100


% increase in size = (0.96)*100

% increase in size = 96%


>>> the final answer is:

The area of the larger circle is 96% greater than the area of the smaller circle.




Thanks for writing.

Staff
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