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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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?
To solve this problem, let's go through the steps:
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:
where is the side length of the square. Thus:
Solving for , we find:
Step 2: To find the volume of the cuboid, we use the formula:
The base area is:
However, the height 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.
No
Calculate the volume of the rectangular prism below using the data provided.
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.
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.
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.
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.
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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