Author Archives: hangtime
Geometric Probability
If you found this video, you probably know that these are problems where they give you some shapes or a shaded region, and you're supposed to figure out the probability that a randomly-landing object (bug, dart, bird poop, etc) will land in one region. This video covers these problems, and also the one common mistake you don't want to make.
This topic covers those problems where they give you a couple shapes, or a shaded region, or a shape inside another shape, or a shape next to a shape with a shaded region in between, and then you're supposed to figure out the probability that a random event (like impact by a bug or lawn dart) will strike one region or the other.
Surface Area Word Problems
The easier problems cover more typical problems you'd see in a regular geometry class, where they're just asking you to find the area of a basketball or pyramid. But then we get into tougher stuff, like calculating the weight of an object by multiplying surface area times density, and how fast the surface area of an object changes when you increase its size.
Surface Area of Spheres
Strangely, spheres are actually the easiest shape to find the surface area of because there aren't a lot of ways for a teacher to make a tricky sphere problem. There's no height to worry about. They can't be oblique. There's no chance you're going to add the sides up wrong. But you should still watch this video, obviously, for the "great circle" discussion if nothing else.
Surface Area of Pyramids & Cones
These are the most confusing surface area problems because there's "slant height" to worry about. How does slant height compare to the height of the prism, and what is the lateral edge? Stick around and learn the answers to these questions and more.
Surface Area of Cylinders
Finding the area of a cylinder is pretty similar to finding the surface area of a prism, though there is a new formula to remember. Plus there's that pi thing.
Surface Area of Prisms
This video covers how to find the surface area of a prism in two ways: 1) the "lateral area" method that uses perimeter; and 2) the way you'll actually remember 3 months from now, which is adding up the surface area from its parts. Also important: how not to find the area of an oblique prism.
These videos cover how to find the surface area of every type of solid: pyramids and cones, oblique and right prisms, spheres, and cylinders. Lots of word problems too.
Volume Word Problems
The previous videos on volume have had lots of word problems, but since we keep getting emails about word problems, this video has even more! Cylinders, density, pipes, spheres, cones, the cost of gravel...
Volume of Spheres
Spheres are kind of all the same -- they're all round. So most of the problems we'll look at in this video cover the more exotic type of questions you can get with spheres, like: spheres inscribed in cylinders, the volume of igloos and scuba tanks, and estimating weight using density.
Volume of Pyramids & Cones
This video covers all the basics of these problems, then gets into the funkier problems such as: volume of pyramids with square and hexagonal bases, cones inscribed in cylinders, using special triangles to find the height, and so much more.
Volume of Cylinders
Cylinders are basically just prisms with circular bases. So we'll skip through the easy problems pretty quick in order to focus on the tricky ones you may see, like cylinders inscribed in spheres, problems where the cylinder is a hole in a cube, and so much more!
Volume of Prisms
This video covers how to find the volume of prisms -- both right prisms and oblique prisms -- including word problems. It also explains some of the common tricks teachers throw at you, like how to find the volume of a pool, where things are not all that they seem.
Converting Volume Units
This video covers the basic units of volume, as well as how to do conversions between them. Also covered are the most common mistake that students make when converting units of volume, which is to use the metric prefixes! If you need ultra-advanced unit conversions, check out the unit conversion videos from chemistry.
This chapter covers regular problems and word problems for how to find the volume of every type of solid: pyramids and cones, oblique and right prisms, spheres, and cylinders. Lots of word problems too, including unit conversions for units of volume: cubic inches, cubic meters, liters, etc.
Volume & Surface Area of Similar 3-D Objects
Based on info about one of the objects -- and perhaps a scale factor -- you're expected to find the surface area and volume of the second object. Also explained is the exponential relationship between scale factors for surface area and volume, and a good way to remember them.
Perimeter & Area of Similar Figures
This video covers the 2-D type of problem, where they give you two similar shapes -- either squares or circles or triangles or amorphous blobs -- and just enough info to figure out the area and perimeter of one based on the other. You won't believe what you have to do with the scale factor for area!
This chapter covers a particular type of problem, where they give you two similar 2-D or 3-D objects -- triangles or polygons or circles or squares or cylinders -- and expect you to figure out the scale factor, area, surface area and volume of one based on the other.
Circle Area Word Problems
How much of a pizza is crust? How much sheetmetal is used in the Hollywood sign? Are circular horse arenas more efficient uses of fencing than square ones? This video answers all these questions, and so many more.