The given diagram represents Edward T. Hall's concept of space surrounding a person defined by 4 nonoverlapping regions. Intimate space is the region inside a circle of radius 1 foot. Personal space is the region within a circle of redius 4 feet but outside Intimate space. Social space is the region within a circle of radius 12 feet but outside personal space. Public space is the region within a circle of radius 25 feet but outside social space. What is the area, in square feet, of the shaded region representing a person's social space?

The correct answer is: 128 π

Hint:
Area of a circle = π r²
Area of shaded region = Area of circle of social space - Area of circle of personal space
Step-by-step solution:-
Radius of circle representing social space = r¹ = 12 feet -------------- (Equation i)
Radius of circle representing personal space = r² = 4 feet --------------- (Equation ii)
As per the given diagram, we observe that-
The shaded region represents the exclusive social space circle of a person i.e.-
Circle of Social space - Circle of Personal space
∴ Area of shaded region = Area of Social space - Area of Personal space
∴ Area of shaded region = π r1² - π r2²
∴ Area of shaded region = π (12)² - π (4)² ------------------------(From Equations i & ii)
∴ Area of shaded region = 144 π - 16 π
∴ Area of shaded region = 128 π sq. ft.
Final Answer:
Option B i.e. 128 π is the correct Option.