student 1: How deserve to we find out just how much a three dimensional object deserve to hold inside (its volume)?

Mentor: Well, over there are different methods for finding volume depending upon the 3 dimensional shape. Let"s an initial look in ~ a box-like shape. How do friend think we must solve for the volume that this shape?

college student 1: Well, we uncover the area the a rectangle through multiplying size times width and that mirrors us exactly how much of a flat rectangle is filled, so maybe we execute something favor that to discover the volume of a three dimensional rectangle-shaped shape?

Mentor:Good thinking! girlfriend are an extremely close. A level shape is referred to as a two-dimensional shape because it has actually two size (in the case of a rectangle lock are referred to as length and width) if a three dimensional form will have three dimensions. Let"s look in ~ a three dimensional rectangular shape (a rectangle-shaped prism):

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Mentor:This shape has a length and also a width just like you mentioned flat rectangles having, however what rather does this 3 dimensional shape have actually that level shapes don"t have? What is the extra dimension?

student 2: over there is an additional side that shows you exactly how deep the is.

Mentor: Right! This is referred to as the depth! The depth is what provides this a 3 dimensional figure since there space three dimensions: length, width, and depth! All three of this dimensions are used to discover the volume of a rectangular prism. To discover the area the a two dimensional rectangle we multiply size by width so allows start v finding the area that a 2 dimensional part of the rectangular prism. Us will very first look at the optimal layer of the rectangle-shaped prism once there is length and also width, yet no depth.

Mentor: What is the length (also sometimes called the height) of this shape?

student 1: 3! There room three cubes follow me the sides going up and also down.

Mentor:Mentor: Great, for this reason the length is 3. Currently what is the width?

college student 2:The broad is 5! there are five cubes follow me the sides going left and also right.

Mentor: the is right! currently we can uncover the area the this flat shape. What execute I perform to uncover the area?

college student 2: You multiply the size (3) through the broad (5). The prize is 15!

student 1: We require to encompass the depth!

Mentor: Right, let"s take an additional look in ~ our 3 dimensional shape:

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Mentor:See the level rectangular shape we looked in ~ is only one great of this huge shape. Think about it prefer this: the level shape that we just looked at is stack on other shapes identical to itself. How numerous of the flat shapes room stacked increase in this 3 dimensional figure?

college student 1:So our third dimension, depth, is 4?

Mentor:Yes. Now, discovering that in the three dimensional form there are 4 layers the the flat shape us looked at, and also knowing that the flat shape has an area that 15 blocks, exactly how do friend think we will find the volume?

student 2: If there are 4 layers, each through an area the 15, us can include 15+15+15+15 and also that will offer us the full volume!

student 1: we could likewise multiply the area the the level shape, 15, by 4. That is the exact same thing as including an area the 15 4 times.

Mentor:Right! and also what execute you obtain when you multiply 15 by 4?

student 1: 60! The volume of the rectangular prism is 60!

Mentor:Great job! You found the volume the a rectangle-shaped prism. Below are the measures that we took to uncover our answer: size x broad = Area of the flat rectangular shape Area x Depth = Volume the the rectangular prism

Mentor: So, in order to discover the volume of a rectangular prism we multiply size by broad by depth.