Understanding Surface Area and Volume

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 cup, 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!