Find a formula for the described function.Express the surface area of a cube as a function of its volume V.SA(V) = State the domain of SA(V). (Enter your answer using interval notation.)
Question
Find a formula for the described function.Express the surface area of a cube as a function of its volume V.SA(V) = State the domain of SA(V). (Enter your answer using interval notation.)
Solution
The volume V of a cube is given by the formula V = s^3, where s is the length of a side of the cube.
To express the surface area SA of a cube as a function of its volume V, we first need to express s in terms of V. We can do this by taking the cube root of both sides of the equation V = s^3, which gives us s = V^(1/3).
The surface area of a cube is given by the formula SA = 6s^2. Substituting s = V^(1/3) into this formula gives us SA(V) = 6(V^(1/3))^2 = 6V^(2/3).
The domain of SA(V) is all real numbers V such that V > 0, because the volume of a cube cannot be negative or zero. In interval notation, this is (0, ∞).
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