Topics Exercises

Up until now, we've explored the world in two dimensions. Area, shapes, and x-y plots are all good and fine, but they're a little flat, aren't they? After all, you can't really play Minecraft in tw...

We've calculated the lateral area for both prisms and cylinders. Lateral area is part of surface area, but it doesn't tell the whole story. We need the bases, too.No, not those bases.The surface ar...

No offense to prisms and cylinders. They're great. But we don't eat our ice cream out of prisms while touring the Egyptian Cylinders of Giza. What we're saying is that there's no substitute for pyr...

We've covered pyramids (literally, since we found the surface area), and now it's time to cover cones (literally, since we'll find the surface area).A right cone is a cone where the axis is also th...

If you play basketball, eat oranges, or have eyeballs (which are sort of necessary to read this), you've most likely encountered spheres at some point in your life. They're common everyday objects,...

For prisms, the fastest way to find the volume is to multiply the area of the base (whatever it is) times the height.V = BhThat's all volume is: base times height Sample ProblemWhat is the volum...

The volume formula works not only for prisms, but for cylinders, too. The only difference is that the base is circular instead of triangular or rectangular or whatevular. If that's true (which it t...

Although we might wonder how much tinfoil it takes to cover the Egyptian pyramids, finding out how many mummies fit inside it would be much more interesting. Provided they don't form an undead army...

The same formula we used for pyramids (V = ⅓Bh) applies to cones, only the base isn't a polygon anymore. It's a circle. Formula-wise, that means we replace B with πr2. That's it. Sample Prob...

Everyone knows the moon isn't really made of cheese. But what if it were? Picture it. Sure, we'd have a bit of an issue with the ocean tides, but think of all that cheese. We could end world hunger...

By now, we've earned quite a bit of street cred working with surface area and volumes. You could throw us any shape and we'd give you its surface area, volume, and even its pants size.What we need...

Two-dimensional shapes have an x-y plane to go home to at the end of the day, and what do the solids have? Nothing. Three-dimensional shapes have been homeless for such a long time, they've begun t...