To find the volume of a right rectangular prism, you can use different methods, though the standard formula is the most common. Let's go over two approaches:

Method 1: Using the Standard Formula

The volume of a right rectangular prism is calculated using the formula: $V = l \times w \times h$ Where:

• $l$ is the length,
• $w$ is the width,
• $h$ is the height.

Given the dimensions:

• $l = 9 \, \text{cm}$,
• $w = 7 \, \text{cm}$,
• $h = 12 \, \text{cm}$,

Substitute the values into the formula: $V = 9 \, \text{cm} \times 7 \, \text{cm} \times 12 \, \text{cm}$ $V = 756 \, \text{cm}^3$

So, the volume of the rectangular prism is 756 cubic centimeters.

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Method 2: Breaking the Prism into Smaller Units

If you want to visualize it, think of the prism as made up of smaller cubes. You can find the volume by determining how many smaller unit cubes (1 cm³) fit inside the entire prism.

To do this:

1. Find the volume of a single cube with side length of 1 cm: This cube has a volume of 1 cm³.
2. Consider how many 1 cm³ cubes fit along each dimension:
   • Along the length (9 cm), you have 9 cubes.
   • Along the width (7 cm), you have 7 cubes.
   • Along the height (12 cm), you have 12 cubes.

Multiply these together to find the total number of 1 cm³ cubes: $\text{Total cubes} = 9 \times 7 \times 12 = 756 \, \text{unit cubes}.$

So again, the volume of the prism is 756 cubic centimeters.

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Would you like further explanation on either of these methods? Here are a few related questions to dive deeper into the topic:

1. What would happen to the volume if one of the dimensions was doubled?
2. How does the volume change if the shape is a square prism (i.e., when two dimensions are the same)?
3. How do you calculate the surface area of a rectangular prism?
4. Can the formula for volume be used for irregular prisms? If not, how do you handle those?
5. How is volume related to other geometric properties, like surface area or the shape of the prism?

Tip: Always visualize the shape as a collection of smaller unit cubes to help understand how the volume formula works.