Express the surface area of a cube as a function of its volume.

Question

Express the surface area of a cube as a function of its volume.

I did this and got A=6V^(2/3)
That is the formula I got for the described function. However, I also need to find its domain... how do I do this?

Answer 1

Here you have

A(V)=6V^(2/3)
where A is the surface area function and the independent variable is V.
The domain is what values can V take, mathematically and logically.
Mathematically, it is possible to calculate V^(2/3) for V∈ℝ.
Logically, V represents the volume of a solid, which cannot take up negative values.
Can you now suggest the domain of V?

Answer 2

So the domain would be all real numbers greater than or equal to 0?

Answer 3

To find the domain of a function, you need to determine the valid inputs or values for the function. In this case, we are given the relationship between the surface area (A) and the volume (V) of a cube.

The formula you obtained is A = 6V^(2/3). To determine the domain of this function, we should consider any limitations or restrictions that might apply.

In the context of a cube, both the surface area and volume must be non-negative since they represent physical measurements. Therefore, the domain should consist of all non-negative real numbers.

So, the domain of this function is: V ≥ 0.

This means that any non-negative volume value can be used as input to the function to calculate the corresponding surface area.

Express the surface area of a cube as a function of its volume.

Here you have

So the domain would be all real numbers greater than or equal to 0?

Correct.

To find the domain of a function, you need to determine the valid inputs or values for the function. In this case, we are given the relationship between the surface area (A) and the volume (V) of a cube.