Calculate Cuboid Volume: Square Base with 24cm Perimeter Challenge

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

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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

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.

121212888555

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