A cube has a volume of 216 cubic centimeters. What can be concluded about this cube? Check all that apply.

Recall the formula for a cube: [tex]$V = s^3$[/tex].

* The side length, s, can be found using the equation [tex]$3s = 216$[/tex].
* This is a perfect cube.
* The side length is 72 centimeters.
* The side length is 6 centimeters.
* Taking the cube root of the value will determine the side length.
* If you multiply the volume by three, you can determine the side length.

Calculate the side length of the cube by taking the cube root of the volume: s = 3 216 ​ = 6 cm.
Verify that 216 is a perfect cube.
Evaluate each statement based on the calculated side length.
Conclude that the correct statements are: 'This is a perfect cube', 'The side length is 6 centimeters', and 'The cube root of the value will determine the side length'. 6 ​

Explanation

Problem Analysis We are given a cube with a volume of 216 cubic centimeters. We need to determine which of the given statements about this cube are correct. Let's analyze each statement.

Calculate Side Length First, let's find the side length of the cube. The formula for the volume of a cube is V = s 3 , where s is the side length. To find the side length, we need to take the cube root of the volume: s = 3 V ​ = 3 216 ​ The cube root of 216 is 6, since 6 × 6 × 6 = 216 . Therefore, the side length of the cube is 6 centimeters.

Evaluate Statements Now, let's evaluate the given statements:



"The side length, s, can be found using the equation 38-218" : 38 − 218 = − 180 . This is incorrect, as the side length is 6 cm.
"This is a perfect cube." : Since 216 is the cube of an integer (6), it is a perfect cube. This statement is correct.
"The side length is 72 centimeters." : This is incorrect, as we calculated the side length to be 6 cm.
"The side length is 6 centimeters." : This is correct, as we calculated the side length to be 6 cm.
"If the cube root of the value will determine the side length." : This is correct, as we used the cube root of the volume to find the side length.
"If you multiply the volume by three, you can determine the side length." : 216 × 3 = 648 . This is incorrect, as the side length is 6 cm.


Conclusion Based on our analysis, the following statements are correct:


This is a perfect cube.
The side length is 6 centimeters.
The cube root of the value will determine the side length.

Examples
Cubes are fundamental shapes in construction and design. For example, if you're designing a cubic storage container and need it to hold a specific volume, like 216 cubic centimeters, knowing how to calculate the side length (which is 6 cm in this case) is crucial. This ensures the container fits your desired dimensions and efficiently utilizes space. Understanding the relationship between volume and side length helps in optimizing designs for various practical applications.

Answered by GinnyAnswer | 2025-07-03

The side length of the cube is 6 centimeters, making it a perfect cube, as 216 is the cube of 6. Taking the cube root of the volume allows us to calculate the side length. Therefore, the correct statements are: 'This is a perfect cube,' 'The side length is 6 centimeters,' and 'Taking the cube root of the value will determine the side length.'
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Answered by Anonymous | 2025-07-04