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Hi, I’m Rob. Welcome to Math Antics! In this lesson, we’re going to learn about another important geometry quantity called Volume. Specifically, we’re going to learn what volume is, and what kind of units we used to measure volume, and how we can calculate the volumes of a few simple geometric shapes. The first thing you need to know is that Volume is a quantity that all 3-Dimensional objects have, but to understand what it means, it will help if we back up just a little and start out with a 1-Dimensional object like this line segment. To measure a 1-Dimensional object we need a 1-Dimensional quantity which we usually call “length”. The length of this line happens to be exactly one centimeter (which is a common unit for measuring length×. And in the Math Antics video about area, we saw that if we move (or extend) this 1-Dimensional line in a direction perpendicular to it by a distance of one centimeter, it forms a 2-Dimensional object called a square. 2-Dimensional objects are measured by the 2-Dimensional quantity that we call area. Because the original line was one centimeter long, and we extended it a distance of one centimeter, the amount of area that this square occupies is one “square centimeter” (which is a common unit for measuring area.) Okay now, imagine that we take that 2-Dimensional square and move (or extend) it in a direction perpendicular to its surface by a distance of 1 centimeter. It forms a 3-Dimensional object that’s called a cube. And to measure a 3-Dimensional object like this, we use the 3-Dimensional quantity called volume. Volume tells us how much 3-Dimensional space (or 3D space) an object occupies. Alright, but how much volume does this cube have? Well, since it was made by extending 1 square centimeter a distance of one centimeter in the 3rd dimension, we say that its volume is exactly one “cubic centimeter” (which is a common unit for measuring volume.) So “square units” are used to measure area, and “cubic units” are used to measure volume. Since square units are made by multiplying TWO 1-Dimensional units together, like centimeter times centimeter, we can abbreviate them using the exponent notation “centimeters to the 2nd power” or “centimeters squared”. And since cubic units are made by multiplying THREE 1-Dimensional units together, like centimeter times centimeter, we can abbreviate them using exponent notation: “centimeters to the 3rd power” or “centimeters cubed”. And, just like there were different sizes of square units like square inches, square meters or square miles, there are also different sized cubic units like cubic inches, cubic meters or cubic miles. See how area and square units are related to volume and cubic units? And there’s another similarity too. Do you remember how you can use square units to measure the area of ANY 2D shape, not just squares? Well, you can use cubic units to measure the volume of ANY 3D shape, not just cubes. To see how that works, take a look at this 2D circle and this 3D...
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