Final answer:
The equation representing that p varies directly with q and the cube of r is p = kqr³, where k is a constant of proportionality.
Step-by-step explanation:
The equation you are looking for is one that expresses direct variation between p and two other variables, q and the cube of r (r³). To say that 'p varies directly with q and the cube of r' means that p is equal to the product of a constant (k), q, and r³. Therefore, the equation can be written as p = kqr³.
For example, if you know the value of q, r, and the constant of proportionality k, you would be able to find p by plugging the values into the equation. Conversely, when all variables but one are known, algebra can be employed to determine the unknown variable. This equation demonstrates a relationship where if either q or r³ changes, p will change proportionally.