Solve for X: Finding the Missing Dimension in a 75 cm³ Cuboid

Q: Why can't I just divide 75 by 4 to find the other dimensions?

Dividing gives you $ 75 ÷ 4 = 18.75 $, but this represents the product of the other two dimensions, not their individual values. For example, the dimensions could be 3×6.25, 5×3.75, or countless other combinations!

Q: What information would I need to solve for X?

You'd need one more dimension of the cuboid. With two dimensions known, you could use $ V = l \times w \times h $ to find the third dimension.

Q: How do I recognize when a problem is unsolvable?

Count your unknowns versus your equations. For volume problems, you need 3 dimensions but only have 1 equation. If you have more unknowns than equations, the problem typically has no unique solution.

Volume Formulas with Insufficient Information

The volume of the cuboid in the figure is 75 cm³.

Calculate the value of X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:04 We'll use the formula for calculating box volume

00:07 height times length times width

00:12 We'll substitute appropriate values and solve for X

00:26 We don't have enough data to know, therefore there's no solution

00:38 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The volume of the cuboid in the figure is 75 cm³.

Calculate the value of X.

Step-by-step solution

Given the problem of determining the value of $X$ with only partial data, it is crucial to understand that the volume of a cuboid is determined by multiplying its three dimensions. Here, we have a volume of 75 cm³ and one dimension given as 4 cm. However, without information about the other dimension(s), determining $X$ is speculative.

Recognizing that the volume $V = l \times w \times h$ and only having one dimension given (which may be part of $4$ ), it is not possible to isolate or solve for the other unknowns only keeping $X$ as unknown.
The figure does not provide complete information about the dimensions that would be used along with the volume to solve for any missing side or dimension directly.

Therefore, as a solution, it must be concluded that without additional information, we cannot solve for $X$ definitively.

The correct answer to the problem is: Impossible to know.

Final Answer

Impossible to know.

Key Points to Remember

Essential concepts to master this topic

Volume Formula: For cuboids, $V = l \times w \times h$ requires all three dimensions
Analysis Technique: With volume 75 cm³ and one dimension 4 cm, we need two more dimensions
Check Requirements: Count given dimensions - only 1 of 3 needed means unsolvable ✓

Common Mistakes

Avoid these frequent errors

Assuming missing dimensions can be found with partial information
Don't try to solve $75 = 4 \times w \times h$ for specific values of w and h = infinite possible solutions! One equation with two unknowns has no unique answer. Always check that you have enough information to solve the problem completely.

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

Why can't I just divide 75 by 4 to find the other dimensions?

Dividing gives you $75 ÷ 4 = 18.75$ , but this represents the product of the other two dimensions, not their individual values. For example, the dimensions could be 3×6.25, 5×3.75, or countless other combinations!

What information would I need to solve for X?

You'd need one more dimension of the cuboid. With two dimensions known, you could use $V = l \times w \times h$ to find the third dimension.

How do I recognize when a problem is unsolvable?

Count your unknowns versus your equations. For volume problems, you need 3 dimensions but only have 1 equation. If you have more unknowns than equations, the problem typically has no unique solution.

Is 'Impossible to know' really a valid mathematical answer?

Absolutely! Recognizing when a problem lacks sufficient information is a crucial mathematical skill. It shows you understand the requirements for solving different types of problems.

Could X represent something other than a dimension?

Even if X represents area or another measurement, you still need more information. The diagram and problem context suggest X is a dimension, but regardless, insufficient data means no unique solution exists.

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