11 - Area inside a circle but outside three other externally tangent circles

Problem 11
Three identical circles of radius 30 cm are tangent to each other externally. A fourth circle of the same radius was drawn so that its center is coincidence with the center of the space bounded by the three tangent circles. Find the area of the region inside the fourth circle but outside the first three circles. It is the shaded region shown in the figure below.
 

011-three-tangent-circles.gif

 

10 Swimming pool in the shape of two intersecting circles

Situation
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