Solution: Original radius $ r = \sqrt{\frac{100\pi}{\pi}} = 10 \, \text{km} $. New radius $ r' = 8 \, \text{km} $. Original area $ 100\pi $, new area $ \pi (8)^2 = 64\pi $. The decrease is $ 100\pi - 64\pi = \boxed{36\pi} \, \text{km}^2 $.

["Title: Understanding Area Changes: A Simple Calculation of Original and New Radius Radii in Square Kilometers", "Meta Description:\nDiscover how to calculate area decrease using original and new radius values. Learn the step-by-step breakdown—from original radius $ r = \sqrt{\frac{100\pi}{\pi}} = 10 , \ ext{km} $ to new radius $ r' = 8 , \ ext{km} $, resulting in a circular area reduction of $ \boxed{36\pi} , \ ext{km}^2 $. Perfect for geometry students and problem solvers.", "---", "### The Geometry of Circles: Area, Radius, and Change", "Understanding how area changes with radius is fundamental in geometry—especially when dealing with circles. Whether applied in engineering, architecture, or environmental studies, knowing how to compute area differences saves time and ensures accuracy. This article breaks down a clear, real-world example: calculating the decrease in area when a circle’s radius shrinks, using radius values in kilometers and square kilometers as units.", "Original Radius:\nThe formula for the area of a circle is:\n[\nA = \pi r^2\n]\nGiven $ r = \sqrt{\frac{100\pi}{\pi}} $, simplify the expression:\n[\nr = \sqrt{\frac{100\pi}{\pi}} = \sqrt{100} = 10 , \ ext{km}\n]", "Now calculate the original area:\n[\nA_{\ ext{original}} = \pi (10)^2 = 100\pi , \ ext{km}^2\n]", "New Radius:\nWhen the radius decreases to $ r' = 8 , \ ext{km} $, the new area becomes:\n[\nA_{\ ext{new}} = \pi (8)^2 = \pi \cdot 64 = 64\pi , \ ext{km}^2\n]", "Area Decrease:\nThe difference in area—how much the circular region has decreased—is:\n[\n\Delta A = A_{\ ext{original}} - A_{\ ext{new}} = 100\pi - 64\pi = \boxed{36\pi} , \ ext{km}^2\n]", "Why This Matters:\nThis straightforward approach showcases a core geometric principle: area scales with the square of radius. Even a small reduction in radius from 10 km to 8 km leads to a noticeable drop in space—measured precisely as $ 36\pi , \ ext{km}^2 $, or approximately 113.1 square kilometers. Such calculations are essential in real-world applications, from urban planning to ecological studies.", "Conclusion:\nBy assigning clear values and systematically applying the area formula, any change in circular dimensions—especially radius reductions—can be accurately quantified. From $ 100\pi , \ ext{km}^2 $ to $ 64\pi , \ ext{km}^2 $, the area decreased by $ \boxed{36\pi} , \ ext{km}^2 $, proving how simple algebra underpins precise spatial analysis.", "---", "Keywords:\ncircle area calculation, radius change area difference, π area formula, geometric area decrease, original radius math, new radius geometry, circular area change, math problem solution, coordinate-based geometry example, decrease in area via radius"]