Solve for X in the Cuboid Volume Equation: 45 = 2.5 × 4 × X

Q: Why do I multiply length and width before dividing?

The volume formula is V = l × w × h, so to find the missing height, you need X = V ÷ (l × w). Think of it as undoing multiplication - you divide by the product of the known dimensions.

Q: What's the difference between area and volume?

Area is 2D (length × width), while volume is 3D (length × width × height). Volume tells you how much space is inside the shape, measured in cubic units.

Q: Can I solve this problem differently?

Yes! You could set up the equation $ 2.5 \times 4 \times X = 45 $ and solve for X. This gives the same answer but shows the algebraic approach more clearly.

Cuboid Volume with Algebraic Rearrangement

The volume of a cuboid is 45.

Its width is 4 and its length is 2.5.

Calculate the value of X.

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The volume of a cuboid is 45.

Its width is 4 and its length is 2.5.

Calculate the value of X.

Step-by-step solution

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

Step 1: Identify the given information.
Step 2: Apply the rearranged volume formula to solve for the missing dimension.
Step 3: Perform the necessary calculations to find $X$ .

Now, let's work through each step:

Step 1: The problem gives us:

Volume of the cuboid, $V = 45$
Width, $w = 4$
Length, $l = 2.5$

Step 2: We'll use the formula for the volume of a cuboid, rearranged to solve for height $X$ :

$X = \frac{V}{l \times w}$

Step 3: Substitute the given values into the formula:

$X = \frac{45}{2.5 \times 4}$

Calculate $2.5 \times 4 = 10$ .

Now, divide the volume by this product:

$X = \frac{45}{10} = 4.5$

Therefore, the solution to the problem is $X = 4.5$ .

Final Answer

4.5

Key Points to Remember

Essential concepts to master this topic

Volume Formula: V = length × width × height for all rectangular prisms
Technique: Rearrange to X = V ÷ (length × width) = 45 ÷ (2.5 × 4)
Check: Verify that 2.5 × 4 × 4.5 = 45 cubic units ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply length and width first
Don't divide volume by each dimension separately like 45 ÷ 2.5 ÷ 4 = wrong answer! This changes the order of operations and gives an incorrect result. Always multiply the known dimensions first, then divide the volume by that product.

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 I multiply length and width before dividing?

The volume formula is V = l × w × h, so to find the missing height, you need X = V ÷ (l × w). Think of it as undoing multiplication - you divide by the product of the known dimensions.

What if I get a decimal answer like 4.5?

Decimal answers are completely normal for cuboid problems! Real-world measurements often involve decimals. Just make sure to check your arithmetic and verify your answer.

How can I remember which dimension is which?

It doesn't matter which you call length, width, or height! The volume formula works the same way regardless of labels. Just make sure you use all three dimensions correctly.

What's the difference between area and volume?

Area is 2D (length × width), while volume is 3D (length × width × height). Volume tells you how much space is inside the shape, measured in cubic units.

Can I solve this problem differently?

Yes! You could set up the equation $2.5 \times 4 \times X = 45$ and solve for X. This gives the same answer but shows the algebraic approach more clearly.

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