Perimeter of the curve $r = 4(1 + \sin \theta)$ by integration

What is the perimeter of the curve r = 4(1 + sin θ)?



The answer is 32 units. For detailed solution, follow the link by clicking on the figure.

10 Swimming pool in the shape of two intersecting circles

A swimming pool is shaped from two intersecting circles 9 m in radius with their centers 9 m apart.

Part 1: What is the area common to the two circles?
A. 85.2 m2
B. 63.7 m2
C. 128.7 m2
D. 99.5 m2

Part 2: What is the total water surface area?
A. 409.4 m2
B. 524.3 m2
C. 387.3 m2
D. 427.5 m2

Part 3: What is the perimeter of the pool, in meters?
A. 63.5 m
B. 75.4 m
C. 82.4 m
D. 96.3 m

Common Quadrilaterals




Area, $A = a^2$

Perimeter, $P = 4a$

Diagonal, $d = a\sqrt{2}$


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