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2Question: A historian of science is analyzing an ancient manuscript describing a right circular cone used in early celestial models. If the cone has a height of $ 3x $ units and a base radius of $ x $ units, what is the ratio of its volume to the volume of a sphere with radius $ x $?
Question: A hydrologist is modeling a reservoir shaped like a hemisphere with radius $ 6x $ units and comparing it to a cylindrical tank of the same radius and height $ 6x $. What is the ratio of the volume of the hemisphere to the volume of the cylinder?
Question: A technology consultant is designing a data center layout and models a storage unit as a cube with side length $ 2x $, and a backup unit as a sphere inscribed within the cube. What is the ratio of the volume of the inscribed sphere to the volume of the cube?
New side length: $ s = 16 - 2 = 14 $
Question: A hydrologist models a reservoir as a cone with base radius $ 5x $ and height $ 12x $, and a cylindrical tank with radius $ 5x $ and height $ 12x $. What is the ratio of the cones volume to the cylinders volume?