Calculate Cuboid Volume: Given 5cm Width, 7cm Height, Missing Length

Q: Why can't I just use the two dimensions I have?

Volume measures 3-dimensional space, so you need all three measurements! With only width (5cm) and height (7cm), you're missing the crucial third dimension - length.

Q: Could I calculate area instead of volume?

Yes! You could find the cross-sectional area using width × height = 5 × 7 = 35 cm², but this isn't the volume the question asks about.

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

Count the given dimensions! For volume, you need exactly 3 measurements. If any dimension is missing or unclear, the volume cannot be determined.

Q: What's the difference between 2D and 3D calculations?

2D (Area): Uses 2 dimensions (length × width)3D (Volume): Uses 3 dimensions (length × width × height)Missing any required dimension makes the calculation impossible!

Volume Formulas with Missing Dimensions

A cuboid is 5 cm wide and 7 cm high.

Is it possible to calculate the volume of the cuboid?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the volume of the box if possible

00:04 We will use the formula to calculate the box volume

00:07 Height times length times width

00:11 We'll substitute appropriate values and solve for the volume

00:17 It seems we don't have enough data to calculate the box volume

00:21 And this is the solution to the question

Step-by-step written solution

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Understand the problem

A cuboid is 5 cm wide and 7 cm high.

Is it possible to calculate the volume of the cuboid?

Step-by-step solution

To solve this problem, we must use the volume formula for a cuboid, which requires the length, width, and height. The given dimensions are:

Width ( $w$ ) = 5 cm
Height ( $h$ ) = 7 cm

The formula for the volume of a cuboid is $V = l \times w \times h$ , where $l$ represents the length, $w$ the width, and $h$ the height.

Based on the problem statement, only the width and height of the cuboid are provided. The length ( $l$ ) is not specified. Therefore, it is not possible to calculate the volume of the cuboid without the third dimension. Thus, we cannot use the volume formula as it requires all three dimensions.

Therefore, it is not possible to calculate the volume of the cuboid with the information given.

The correct answer is No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula Requirements: Volume needs all three dimensions: length, width, height
Technique: Use $V = l \times w \times h$ only when l, w, h are known
Check: Count given dimensions: 5cm width, 7cm height, missing length ✓

Common Mistakes

Avoid these frequent errors

Attempting to calculate volume with incomplete information
Don't try to use V = l × w × h when length is missing = impossible calculation! The formula requires exactly three dimensions, not two. Always verify that length, width, AND height are all provided before attempting volume calculations.

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 use the two dimensions I have?

Volume measures 3-dimensional space, so you need all three measurements! With only width (5cm) and height (7cm), you're missing the crucial third dimension - length.

What if I assume the length is the same as width?

Never make assumptions about missing measurements! The problem doesn't say it's a cube or give any hints about length. Only work with the information provided.

Could I calculate area instead of volume?

Yes! You could find the cross-sectional area using width × height = 5 × 7 = 35 cm², but this isn't the volume the question asks about.

How do I recognize when a volume problem is unsolvable?

Count the given dimensions! For volume, you need exactly 3 measurements. If any dimension is missing or unclear, the volume cannot be determined.

What's the difference between 2D and 3D calculations?

2D (Area): Uses 2 dimensions (length × width)
3D (Volume): Uses 3 dimensions (length × width × height)
Missing any required dimension makes the calculation impossible!

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