Volume of a sphere to calculate the capacity of your lungs
Just a quick idea here… To make a lesson on calculating the volume of a sphere contextually meaningful how about using a balloon to calculate the capacity of your lungs? Get a pupil to take a deep breath and then fully exhale into a balloon. Then measure the radius of the balloon and calculate the volume. You’ll need too get balloons that form spherical shapes for it to work well.
An interesting chat about the accuracy of the results could follow. Is the surface tension of the balloon similar to that of your lungs? Is it an over estimate or under estimate and why? Etc…
As an extension, how about relating the volume of a sphere to that of a cylinder? Archimedes’ famous cylinder and circumscribed sphere discovery states the volume of a sphere circumscribed inside a cylinder is 2/3 the volume of the cylinder. Compare the formulae; can you prove it!?