Final answer:
To solve for A(m) in terms of pressure and volume, the function R(m) needs to be integrated with the volume relationship m = pAh and combined with the initial pressure and volume parameters, P1 and V1, to establish a relationship between P(m) and A(m).
Step-by-step explanation:
To find the formula for the function A(m) where A(m)=P(π(m)), it's important to understand the given context regarding pressure and volume. We are provided with the function R(m) which represents pressure, and we're given a volume relationship m = pAh, where m is the mass, p is the density, A is the cross-sectional area, and h is the depth. To connect P(m) and A(m), we need to integrate the given formulas and relationships, using pressure P, volume V, and area A.
Given the initial pressure P1 and initial volume V1, we can relate these to a second pressure and volume, P2 and V2, respectively. To solve for A(m), we could use the definition of pressure (P = F/A), or manipulate other equations referencing pressure such as Π = MRT, where Π represents osmotic pressure rather than mechanical pressure, to find a function that defines how A changes with m.