1. Module 1

1.12. Page 2

Mathematics 10-3 Module 1 Lesson 3

Module 1: The International System of Units (SI)

 

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prism: in geometry, a 3-D object that has two congruent and parallel faces (the top and bottom bases) and lateral faces that are parallelograms

 

Such a 3-D object is also known as a rectangular box. The following is a 3-D object known in geometry as a prism.

 

This is a drawing of a 3-D geometric object known as a prism or a rectangular box.

Suppose you wanted to determine the dimensions of a (rectangular) prism-shaped container that would hold exactly 24 sugar cubes with no wasted space. The cubes would have to be packed one against the other and tightly against the walls of the container. What would the dimensions of the box depend upon?

 

This is a drawing of a rectangular object made up of 24 sugar cubes.

 

The diagram illustrates one possible prism-shaped arrangement. How many sugar cubes are there in the bottom layer?

 

How do you know there are 24 cubes altogether?

 

Think of a box made of thin cardboard, just large enough to hold this arrangement of cubes. You can then describe the dimensions of this box—4 cubes long, 2 cubes wide, and 3 cubes high. What would you get if you multiplied 4, 2, and 3 together?

 

volume: a measurement of how many cubic units into which an object or space may be divided

 

For example, if your living room is 5 m long by 3 m wide by 3 m high, its volume is
5 m × 3 m × 3 m = 45 m3.

 

This is a drawing of a 3-D grid that is 5 m long, by 3 m wide, by 3 m high.

So, the volume of the box = length × width × height.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The total number of sugar cubes is 4 × 2 × 3 = 24. The total number of cubes is found by multiplying length × width × height.
There are 3 identical layers of 8 cubes, and 3 × 8 = 24.
There are 8 cubes in the bottom layer because there are 2 rows of 4 cubes each, and 2 × 4 = 8.
The dimensions of the box would depend on the size of the sugar cubes and how the cubes were arranged in the box.