Formulas

Area of Pyramids and Cones

We’ve looked at the volume of a pyramid, the formula for which can be found geometrically by a couple very different methods. Cones can be handled the same way, so we can skim over them. Let’s finish up by considering the surface areas of both cones and pyramids. Volumes and areas I’ll start with a …

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Volume and Surface Area of a Sphere – Without Calculus

We often get questions about deriving formulas for area and volume; usually when the question is about a sphere, the context is calculus, so we talk about integration, the usual modern method. But for students who only know geometry, “wait until you learn calculus” can be unsatisfying. Fortunately, there are a couple ways to do …

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Summing Divisors

In searching for answers about counting divisors over the last couple weeks, I found a few that are about the similar question of finding the sum of a number’s divisors. In fact, a couple questions and answers confuse the two problems. Let’s finish off the topic by looking at these. (Keep in mind that “divisor” …

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Counting Divisors of a Number

How many divisors (also called factors) does a number have? We’ve answered many questions about that over the years, sometimes by just guiding a student to discover it, sometimes either deriving the formula for them or just showing and using it. Let’s look at a few. Discovering the trick We’ll start with a question from …

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Rank of a Binary Number

(A new question of the week) A few months ago, I wrote about Ranking a Word Among Its Permutations, that is, finding where a word would be found in an ordered list of all possible “words” made by permuting its letters. The problem in general requires a (sometimes lengthy) algorithm. A month or so later, …

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