Marco is shopping at Star Foods and finds that the Texas grapefruits have twice the diameter of the Florida ones, but cost seven times as much. Recalling that the volumes of similarly shaped solids vary directly with the cube of a linear dimension, in this case the diameter, Marco instantly determines which grapefruit gives him more for the money. Which one does Marco choose and why?
What is the volume of the Florida grapefruit?
What is the radius of the Texas grapefruit in terms of the Florida radius?
So which is the better deal?