Mathematics

Mathematics

Problem

For

\theta

in

[0,\pi]

consider the region

S(a)

bounded between the curves

r=a\sin\theta

(outer curve) and

r=2\sin\theta

(inner curve), where

a>2

. When

a=5

, the area of the region is

A

. For which of the following values of

a

will the area of the region be

1.5A

? a)

a=6

b)

a=4\sqrt{2}

c)

a=\sqrt{35.5}

d)

a=7

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