Bunuel wrote:

If the radius of the circle H in the figure above is 2/3 of the radius of the circle G, and the radius of circle G is 3/4 of the radius of the circle F, then the area of the shaded region is what part of the area of circle F?

(A) 1/12

(B) 17/144

(C) 1/4

(D) 5/16

(E) 9/16

Attachment:

2017-11-13_1910.png

Radii for H, G, and F:

\(H = \frac{2}{3}G\)

\(\frac{H}{G}=\frac{2}{3}\)

\(H = 2, G = 3\)

\(G = \frac{3}{4}F\)

\(3=\frac{3}{4}F\)

\(F = 4\)

Area of H = \(\pi*r^2= 4\pi\)

Area of G = \(9\pi\)

Area of F = \(16\pi\)

Shaded region's area = (Area of G) - (Area of H)

\((9\pi - 4\pi) = 5\pi\)

Area of the shaded region is what part of the area of circle F?

\(\frac{5\pi}{16\pi}=\frac{5}{16}\)

Answer D

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"