#### 810,000Question: A glaciologist models a glacier as a right circular cone with base radius $ 8x $ units and height $ 6x $ units. If a spherical ice chunk of radius $ 2x $ units is extracted from the glaciers center, what is the remaining volume of the glacier?
["### 810,000Question: A glaciologist models a glacier as a right circular cone with base radius $ 8x $ units and height $ 6x $ units. If a spherical ice chunk of radius $ 2x $ units is extracted from the glacier’s center, what is the remaining volume of the glacier?", "As climate discussions grow globally, penguin-sized ice dynamics in Earth’s largest glaciers are drawing quiet attention—especially how volume shifts affect sea-level projections. A powerful geometric model illustrates this: a glacier shaped like a right circular cone, with a base radius of $ 8x $ units and a height of $ 6x $, slowly reveals hidden changes when a spherical ice core, $ 2x $ in radius, is extracted from its center.", "---", "### Why#\nThis model reflects a growing interest in precision glaciology—quantifying how small internal features impact large-scale ice mass. While the cone’s elegant form captures public imagination, the focus here lies in measurable volume: a blend of geometry and Earth science that matters to researchers and climate-conscious readers alike. Understanding these shifts helps predict melt patterns and long-term stability with greater clarity.", "---", "### How Does It Work? \nCalculating the glacier’s original volume begins with a cone formula: Volume = $ \frac{1}{3} \pi r^2 h $. Here, base radius $ r = 8x $, height $ h = 6x $, so:\n$$\n\ ext{Glacier Volume} = \frac{1}{3} \pi (8x)^2 (6x) = \frac{1}{3} \pi (64x^2)(6x) = 128\pi x^3\n$$\nNext, the volume of the spherical ice chunk follows the standard formula $ \frac{4}{3} \pi r^3 $ with radius $ 2x $:\n$$\n\ ext{Extracted Volume} = \frac{4}{3} \pi (2x)^3 = \frac{4}{3} \pi (8x^3) = \frac{32}{3}\pi x^3\n$$\nSubtracting these yields the glacier’s updated volume post-extraction:\n$$\n\ ext{Remaining Volume} = 128\pi x^3 - \frac{32}{3}\pi x^3 = \left("]
