Surface Area and Volume Discussion Mentor: So, if we know that we can find the area of a two-dimensional figure, do you think that it is possible to find the area of a three dimensional figure? In fact, who can tell me what a three dimensional figure is? Student 1: A three dimensional figure is like a ball or a cube--it's not flat. Mentor: That's right. Now, can anyone say something about what it might mean to find the area of such a figure? Student 2: When you say "find the area," do you mean the outside, or all the insides included? Mentor: That's a good question? What do you think? Student 2: Well, it seems like they are two different things... but it might be important to know both of them. I don't know which one would be the area though. Mentor: What if I told you that there is something called surface area? Student 3: That sounds like it would be just the outsides--the area that is on the surface, which I can touch. Mentor: Very well said! So, what do you think the volume is? Student 3: I bet that's when you find a value that includes all the stuff inside! Mentor: Good! Volume is sort of a measure of how much space is inside. Student 4: What do you mean by "the space inside?" Mentor: Well, if I filled up a shape, like a basketball with water and then measured how much water was in it, then I would be measuring the volume. Does that help you see it? Student 4: Oh, I think I see. Volume is a way of saying how much a three dimensional object can hold inside. Mentor: Now you understand!