Three regions are defined in the first quadrant by pairs of concentric circles in…

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Three regions are defined in the first quadrant by pairs of concentric circles in polar form. • Region

A

: between

r=2

and

r=4

for

0\le\theta\le\frac{\pi}{2}

• Region

B

: between

r=3

and

r=4

for

0\le\theta\le\frac{\pi}{2}

• Region

C

: between

r=2

and

r=4

for

0\le\theta\le\frac{\pi}{4}

Rank the areas of the three regions from largest to smallest. (a)

A > C > B

(b)

C > A > B

(c)

A > B > C

(d)

B > A > C