Calculate Cuboid Volume: Square Base with 24cm Perimeter Challenge

Volume Calculations with Missing Dimensions

Given an cuboid so that the base is a square

Given that the perimeter of the base is 24 cm

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
00:03 Square base according to the data, therefore equal sides
00:07 The perimeter of the square equals the sum of its sides
00:12 Let's substitute appropriate values and solve for side A
00:15 This is side A
00:19 Let's draw the box, we can see that we're missing the height of the box
00:26 Let's draw the box
00:30 Since we're missing the box height, we cannot calculate its volume
00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given an cuboid so that the base is a square

Given that the perimeter of the base is 24 cm

Is it possible to calculate the volume of the cuboid?

2

Step-by-step solution

To solve this problem, let's go through the steps:

  • Step 1: Determine the side length of the square base.
  • Step 2: Note that calculating the volume requires the height of the cuboid, which is not given.

Now, let's perform these steps:

Step 1: We know the perimeter of the square base is 24 cm. The formula for the perimeter of a square is:

P=4s P = 4s

where s s is the side length of the square. Thus:

24=4s 24 = 4s

Solving for s s , we find:

s=244=6cm s = \frac{24}{4} = 6 \, \text{cm}

Step 2: To find the volume of the cuboid, we use the formula:

V=Base Area×Height V = \text{Base Area} \times \text{Height}

The base area A A is:

A=s2=62=36cm2 A = s^2 = 6^2 = 36 \, \text{cm}^2

However, the height h h of the cuboid is not provided, which is essential to calculate the volume.

Conclusion: Since the height of the cuboid is unknown, it is impossible to calculate the volume of the cuboid.

Therefore, the solution to the problem is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Volume Formula: Always requires length, width, and height measurements
  • Square Base: Perimeter 24 cm gives side length s=244=6 s = \frac{24}{4} = 6 cm
  • Check Requirements: Volume needs base area AND height - verify all dimensions given ✓

Common Mistakes

Avoid these frequent errors
  • Assuming you can calculate volume with incomplete information
    Don't think finding the base area (36 cm²) means you can find volume = incomplete calculation! You're missing the height dimension. Always check that you have ALL required measurements before attempting volume calculations.

Practice Quiz

Test your knowledge with interactive questions

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

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FAQ

Everything you need to know about this question

I found the base area is 36 cm². Why can't I calculate volume?

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Great work finding the base area! However, volume requires three dimensions. You need: Base Area × Height. Without knowing the height, the volume could be anything from nearly zero to infinitely large.

What if I assume the cuboid is actually a cube?

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Never make assumptions not stated in the problem! The question specifically says cuboid (not cube), so the height could be different from the base dimensions. Only work with given information.

How do I know when I have enough information for volume?

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For cuboids, you need all three dimensions: length, width, and height. For rectangular prisms with square bases, you need the side length and the height.

Is there any way to find the volume from just the perimeter?

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No! Perimeter only tells you about the outline of the base. Many different heights could create cuboids with the same base perimeter but completely different volumes.

What would I need to calculate the volume?

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You'd need one more piece of information: either the height of the cuboid, the total surface area, or some other measurement that involves the height dimension.

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