Filling Cone, Hemisphere and Cylinder: Easy as 1:2:3
Filling a cone, a hemisphere and a cylinder is as easy as 1:2:3, the ratios of their volumes. A display at an interactive science center (the best kind!) consists of three water containers: a cone, hemisphere and cylinder. Visitors can use the cone twice to fill the hemisphere with water, then combine that with a third cone's worth to completely fill the cylinder. This is especially intriguing because of the various-shaped containers. This Demonstration allows the user to interactively fill these containers and gain insight about why their volumes conform to the 1:2:3 ratios. Two related visualizations show that the volume of the cone is 1/2 the volume of the hemisphere and 1/3 that of the cylinder, assuming that their heights are all equal to the radius of the hemisphere.
Kenneth E. Caviness and R. Lewis Caviness, "Filling Cone, Hemisphere and Cylinder: Easy as 1:2:3", from Wolfram Demonstrations Project, http://demonstrations.wolfram.com/FillingConeHemisphereAndCylinderEasyAs123/, June 16, 2020.