Another concrete to abstract example

My older son and I are in the review section on spheres, cylinders, and cones in our Introduction to Geometry book and found a neat problem about cones. The original problem has all numbers, but I thought it would be fun to try to solve it with variables, too. It was interesting to see the jump in difficulty when I took out the numbers.

Before presenting the videos, sorry if the video or sound quality isn’t as good as it usually is. I had to shoot these on an iphone rather than with our camera because of a battery issue.

Here’s the original problem:


and here’s the problem without the numbers:


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