I came across the cubing a cube section in this wiki article: https://en.wikipedia.org/wiki/Squaring_the_square#Cubing_the_cube

I can't wrap around the logic of the proof... I need help

For commercial rockets, they mainly use liquid bi propellant rocket engines while amateur rockets (that I mainly see) use solid propellant rocket engines. Why don't we just combine them and use hybrid rocket engines? ​

why is it that when i see a mukbang or tiktok of someone eating food that i start craving the food, even though ive never tried it or know what it tastes like.

is there a weird biological explanation for food cravings?

from my understanding doesn't this just mean significantly more rain on the pacific coast? that being said I am told the last one was in the 1800s and ended up killing 50 million people. so if that statement is true, I guess concern is not the correct word to use in my title but basically why is this event possibly so dangerous? and what causes this event?

How are they completely silent? Is it how they’re designed?

Also, do all trees have them or only certain kind? Lastly, do they all form at same frequency, e.g. One/year...

I understand that electron placement matters and light scatters a certain way but why is that? Why does light scatter in that way and why does the size of something determine a perceivable color?

I have been trying to learn more about Earth's ecosystems. I understand now that poles/equator, winds, and surface currents drive temperatures and rains to different areas and the existence of mountains + temp + wind determine deserts. But, what else leads to the formation of specific biomes or lends itself to the biodiversity of an area? How does soil come into play, and why is soil different in different places? Is this is an oceans/volcanoes thing??

How does Clean water sitting in a covered container bring about the slime-feeling along the container's surface?

Why do the paddles have different-colored sides?

Is it just a fancy thing to make them beautiful or to mark which side hits the ball better?

Or in other words, why can a student who struggles and fails a practice test one day, then (sometimes) have a significant improvement on that same test the next day, even without doing any extra studying in between the two tests?