U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3

When two quantities, U and V, are inversely proportional, it means that as one of them increases, the other decreases, and vice versa, in such a way that their product remains constant. In mathematical terms, we can express this relationship as U*V^3 = k, where k is a constant. In this problem, we are told that U is inversely proportional to the cube of V. Therefore, we can write U*V^3 = k, where k is a constant of proportionality that we need to find. We are also given that U equals 81 when V equals 2. Substituting these values into the equation, we get: 81*2^3 = k k = 648 Now that we have the constant of proportionality, we can use the equation U*V^3 = 648 to find U when V equals 3: U*3^3 = 648 U*27 = 648 U = 648/27 Simplifying this expression, we get U = 24. Therefore, the answer is 24.