Cuboid Volume Calculation: Analyzing a 5x8x2 Rectangular Prism

Q: Do I need to know which dimension is the height?

No! For volume calculation, it doesn't matter which dimension you call height. The formula $ V = l \times w \times h $ works the same regardless of how you assign the dimensions.

Q: What if I multiply the dimensions in a different order?

You'll get the same answer! Whether you calculate 5 × 8 × 2, or 2 × 5 × 8, or 8 × 2 × 5, the result is always 80 cubic units because multiplication is commutative.

Q: Why does the order not matter in multiplication?

This is called the commutative property of multiplication. It means changing the order of factors doesn't change the product. For example: 3 × 4 = 4 × 3 = 12.

Q: What units should I use for volume?

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

Q: Can this work for any rectangular box?

Absolutely! Any cuboid (rectangular box) volume is calculated by multiplying all three dimensions together, no matter how you arrange or label them.

Volume Calculation with Commutative Property

Given an cuboid whose dimensions are 5,8,2

Indicate whether it is true or false:

To calculate the volume of the cuboid it is not necessary to know the sides of the base and the height.

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given an cuboid whose dimensions are 5,8,2

Indicate whether it is true or false:

To calculate the volume of the cuboid it is not necessary to know the sides of the base and the height.

Step-by-step solution

To solve this problem, we need to determine the volume of the given cuboid. The volume of a cuboid is calculated using the formula:

$V = \text{length} \times \text{width} \times \text{height}$

For the given cuboid with dimensions 5, 8, and 2, the volume is calculated as:

V = 5 \times 8 \times 2 = 80

Notice that regardless of how we assign the roles of length, width, and height to the numbers 5, 8, and 2, the multiplication result remains the same.

This is because multiplication is commutative, meaning the order of factors does not affect the product.

Thus, it is not necessary to identify which dimension is the base sides (length or width) and which is the height; only the product of all three dimensions matters for volume.

Therefore, the statement "To calculate the volume of the cuboid it is not necessary to know the sides of the base and the height." is True.

Final Answer

True

Key Points to Remember

Essential concepts to master this topic

Formula: Volume equals length times width times height
Technique: Multiply all three dimensions: 5 × 8 × 2 = 80
Check: Order doesn't matter: 2 × 5 × 8 = 80 ✓

Common Mistakes

Avoid these frequent errors

Thinking you must identify which dimension is height
Don't worry about labeling dimensions as length, width, or height = wasted time and confusion! The commutative property means order doesn't affect multiplication. Always multiply all three dimensions together regardless of their labels.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Do I need to know which dimension is the height?

No! For volume calculation, it doesn't matter which dimension you call height. The formula $V = l \times w \times h$ works the same regardless of how you assign the dimensions.

What if I multiply the dimensions in a different order?

You'll get the same answer! Whether you calculate 5 × 8 × 2, or 2 × 5 × 8, or 8 × 2 × 5, the result is always 80 cubic units because multiplication is commutative.

Why does the order not matter in multiplication?

This is called the commutative property of multiplication. It means changing the order of factors doesn't change the product. For example: 3 × 4 = 4 × 3 = 12.

What units should I use for volume?

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

Can this work for any rectangular box?

Absolutely! Any cuboid (rectangular box) volume is calculated by multiplying all three dimensions together, no matter how you arrange or label them.

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