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

Recall the formula Cube [tex]V=s^3[/tex].

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

Calculate the side length s of the cube by taking the cube root of the volume: s = 3 216 ​ = 6 cm.
Verify that 216 is a perfect cube since 6 3 = 216 .
Confirm that taking the cube root of the volume determines the side length.
Conclude that the correct statements are: 'This is a perfect cube', 'The side length is 6 centimeters', and 'Taking the cube root of the volume will determine the side length'. 6 ​

Explanation

Problem Analysis We are given a cube with a volume of 216 cubic centimeters, and we need to determine which statements about this cube are correct. The formula for the volume of a cube is V = s 3 , where s is the side length of the cube.

Calculate the Side Length First, let's find the side length of the cube. We have V = s 3 , so 216 = s 3 . To find s , we need to take the cube root of 216: s = 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 the Statements Now, let's evaluate the given statements:



The side length, s , can be found using the equation 3 s = 216 : If 3 s = 216 , then s = 216/3 = 72 . This is incorrect, as we found s = 6 .
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 found the side length to be 6 centimeters.
The side length is 6 centimeters : This is correct, as we calculated s = 6 .
Taking the cube root of the volume will determine the side length : This is correct, as we used the cube root to find s = 3 216 ​ = 6 .
If you multiply the volume by three, you can determine the side length : This is incorrect. Multiplying the volume by three gives 3 × 216 = 648 , which is not the side length.


Conclusion Based on our calculations and analysis, the correct statements are:


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

Examples
Cubes are common in everyday life. For example, dice are cubes, and we can calculate their volume if we know the side length. Also, many boxes are in the shape of a cube or rectangular prism, and understanding volume helps in determining how much a box can hold. Understanding cubes and their volumes is also important in construction and engineering, where cubic shapes are frequently encountered, and their properties must be well understood. For instance, if you're designing a cubic storage container, knowing the relationship between the side length and volume is crucial for determining its capacity. The volume is calculated as V = s 3 , where s is the side length. In our case, the volume of the cube is 216 cubic centimeters, and we found that the side length is 6 centimeters.

Answered by GinnyAnswer | 2025-07-03

The correct statements about the cube are that it is a perfect cube, its side length is 6 centimeters, and taking the cube root of the volume will determine the side length. The incorrect statements include finding the side length using 3 s = 216 , stating the side length is 72 centimeters, and multiplying the volume by three.
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Answered by Anonymous | 2025-07-04