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

 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 www.solving-math-problems.com