Calculate the Volume of a Rectangular Prism: 4 × 5 × 9 Dimensions

Q: Why do we multiply instead of add the dimensions?

Volume measures the space inside a 3D shape. When you multiply length × width × height, you're counting how many unit cubes fit inside. Adding would just give you the total distance around edges, not the space!

Q: What if the dimensions are in different units?

You must convert all dimensions to the same unit before multiplying. For example, if one dimension is in feet and another in inches, convert everything to inches first, then multiply.

Q: Does the order of multiplication matter?

No! You can multiply the dimensions in any order you want: 4×5×9, 5×9×4, or 9×4×5 all give the same answer. Multiplication is commutative.

Q: What units should my answer have?

Volume is always measured in cubic units. If your dimensions are in centimeters, your volume is in cubic centimeters (cm³). If in meters, then cubic meters (m³).

Q: Can I check my answer somehow?

Yes! Make sure your answer makes sense by thinking: Is this volume reasonable for the given dimensions? Also, verify you multiplied correctly: $ 4 \times 5 = 20 $, then $ 20 \times 9 = 180 $.

Volume Formula with Three-Dimensional Measurements

Calculate the volume of the rectangular prism below using the data provided.

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Understand the problem

Calculate the volume of the rectangular prism below using the data provided.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given dimensions of the prism.
Step 2: Apply the formula for the volume of a rectangular prism.
Step 3: Perform the necessary calculations.

Now, let's work through each step:
Step 1: The given dimensions are height $h = 5$ , width $w = 4$ , and depth $d = 9$ .
Step 2: We use the formula for volume $V = h \times w \times d$ .
Step 3: Plugging in our values, we have
$V = 5 \times 4 \times 9 = 180$

Therefore, the volume of the rectangular prism is $180$ .

Final Answer

180

Key Points to Remember

Essential concepts to master this topic

Formula: Volume equals length times width times height
Technique: Multiply all three dimensions: $4 \times 5 \times 9 = 180$
Check: Verify units are cubic and all dimensions were multiplied together ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't add the dimensions like 4 + 5 + 9 = 18! This gives you the perimeter of one face, not volume. Volume measures space inside the prism, which requires multiplying length × width × height to get cubic units. Always multiply all three dimensions together.

Practice Quiz

Test your knowledge with interactive questions

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

FAQ

Everything you need to know about this question

Why do we multiply instead of add the dimensions?

Volume measures the space inside a 3D shape. When you multiply length × width × height, you're counting how many unit cubes fit inside. Adding would just give you the total distance around edges, not the space!

What if the dimensions are in different units?

You must convert all dimensions to the same unit before multiplying. For example, if one dimension is in feet and another in inches, convert everything to inches first, then multiply.

Does the order of multiplication matter?

No! You can multiply the dimensions in any order you want: 4×5×9, 5×9×4, or 9×4×5 all give the same answer. Multiplication is commutative.

How do I know which dimension is which?

It doesn't matter for volume calculation! Whether you call them length, width, and height or use different names, just make sure you multiply all three numbers together.

What units should my answer have?

Volume is always measured in cubic units. If your dimensions are in centimeters, your volume is in cubic centimeters (cm³). If in meters, then cubic meters (m³).

Can I check my answer somehow?

Yes! Make sure your answer makes sense by thinking: Is this volume reasonable for the given dimensions? Also, verify you multiplied correctly: $4 \times 5 = 20$ , then $20 \times 9 = 180$ .

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