gwd 15 31

Kath1985

[attachimg=275,292]85509[/attachimg]
In the figure shown, iftheareaoftheshadedregion is 3 times theareaofthe smaller circular region, then the circumference ofthe larger circle is how many times the circumference ofthe smaller circle?

A. 4
B. 3
C. 2
D. 根號3
E. 根號2
答案是 C....
請問這題怎麼解呢

Kath1985

sdcar2010

area = pai*radius^2

area of the small circle = pai *r^2
area of the big circle = pai*R^2

area of the shade = pai*(R^2 - r^2) = 3*pai*r^2
Therefore, R^2 = 4*r^2, R= 2r

Since circumference = pai*2*radius, it follows that the ratio between the circumferences of the big and small circle is the ration between their radii, which is 2.