## Area for grazing by the goat tied to a silo

Problem
A goat is tied outside a silo of radius 10 m by a rope just long enough for the goat to reach the opposite side of the silo. Find the area available for grazing by the goat. Note that the goat may not enter the silo.
A. 1033.54 m2
B. 2067.08 m2
C. 516.77 m2
D. 2583.86 m2

## 08 Area Enclosed by r = a sin 3θ and r = a cos 3θ

Problem
Find the area bounded by $r = a \sin 3\theta$ and $r = a \cos 3\theta$.

## 07 Area Enclosed by r = 2a cos θ and r = 2a sin θ

Problem
Find the area enclosed by the following:

(a)   $r = 2a \cos \theta$
(b)   $r = 2a \sin \theta$

## 05 Area Enclosed by r = a sin 2θ and r = a cos 2θ

Problem
Find the area bounded by $r = a \sin 2\theta$ and $r = a \cos 2\theta$.

## 04 Area of the Inner Loop of the Limacon r = a(1 + 2 cos θ)

Example 4
Find the area of the inner loop of the limacon r = a(1 + 2 cos θ).

## 03 Area inside the cardioid r = a(1 + cos θ) but outside the circle r = a

Example 3
Find the area inside the cardioid r = a(1 + cos θ) but outside the circle r = a.

## 03 Area Enclosed by Cardioids: r = a(1 + sin θ); r = a(1 - sin θ), r = a(1 + cos θ), r = a(1 - cos θ)

Problem
Find the area individually enclosed by the following Cardioids:
(A)   $r = a(1 - \cos \theta)$
(B)   $r = a(1 + \cos \theta)$
(C)   $r = a(1 - \sin \theta)$
(D)   $r = a(1 + \sin \theta)$

## 02 Area Bounded by the Lemniscate of Bernoulli r^2 = a^2 cos 2θ

Example 2
Find the area bounded by the lemniscate of Bernoulli r2 = a2 cos 2θ.

## 01 Area enclosed by r = 2a sin^2 θ and r = 2a cos^2 θ

Problem
Find the area enclosed by
•  r = 2a sin2 θ
•  r = 2a cos2 θ