Problem

Find a formula for the described function.
Express the surface area of a cube as a function of its volume $V$.
\[
S A(V)=6 V^{\left(\frac{2}{3}\right)}
\]
State the domain of $S A(V)$. (Enter your answer using interval notation.)

Answer

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Answer

Final Answer: The domain of $SA(V)$ is $[0, \infty)$, which is represented as \(\boxed{[0, \infty)}\) in latex typesetting.

Steps

Step 1 :Find a formula for the described function. Express the surface area of a cube as a function of its volume $V$. The formula is $SA(V)=6 V^{\left(\frac{2}{3}\right)}$

Step 2 :State the domain of $SA(V)$. The domain of a function is the set of all possible input values, which produce a valid output from a particular function. In this case, the function is the surface area of a cube, expressed as a function of its volume. The volume of a cube can be any non-negative real number, since a cube cannot have a negative volume.

Step 3 :Therefore, the domain of the function $SA(V)$ is all non-negative real numbers.

Step 4 :Final Answer: The domain of $SA(V)$ is $[0, \infty)$, which is represented as \(\boxed{[0, \infty)}\) in latex typesetting.

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