The side length,s, of a cube is related to its volume, v, by the formula s=v^1/3. A cube box when filled with materials has a volume of 729 cm2. What is the side lenth of the cube box used?
Please help me step by step with this. I don't know where to start :(
You would start by substituting 729 for V in the equation of s=v^1/3, making it 729^1/3.
729^1/3 can be seen as the 3rd root of 729.
Simply type that into your calculator.
The answer once entering the equation in a calculator is S=9.
So, the side length is 9 ~ ^^
Sure, I can help you step by step with this problem.
Step 1: Understand the problem and identify known values
We are given that the volume of a cube, v, is related to its side length, s, by the formula s = v^(1/3). We are also given that the volume of the cube box used is 729 cm^3.
Step 2: Substitute the known values into the formula
Replacing v with 729 cm^3 in the formula, we have s = (729 cm^3)^(1/3).
Step 3: Simplify the expression inside the parentheses
To simplify this expression, we need to find the cube root of 729 cm^3. The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In this case, the cube root of 729 is 9, as 9 x 9 x 9 equals 729.
Step 4: Substitute the simplified expression back into the formula
Now we have s = 9 cm.
Step 5: Find the solution
Therefore, the side length of the cube box used is 9 cm.
In summary:
- Use the formula s = v^(1/3) to relate the side length and volume of a cube.
- Substitute the known value for volume into the formula.
- Simplify the expression inside the parentheses by finding the cube root.
- Substitute the simplified expression back into the formula to find the side length.
- The solution is the side length of the cube box, which in this case is 9 cm.