The pressure 𝑃 of an object is found by dividing the force 𝐹 done by the object by its area 𝐴. Which of the following equations give the force 𝐹 in terms of 𝑃 and 𝐴? A) 𝐹 equals 𝑃 times 𝐴. B) 𝐹 equals 𝑃 divided by 𝐴. C) 𝐹 equals 𝐴 divided by 𝑃. Or D) 𝐹 equals 𝑃 plus 𝐴.
We know that the pressure 𝑃 is — we can write that mathematically as saying 𝑃 equals. We’re dividing the force 𝐹 by the area 𝐴, which means we could say 𝑃 equals 𝐹 divided by 𝐴. Another way to put that 𝑃 equals 𝐹 over 𝐴. And we want this equation to be 𝐹 equal to something, 𝐹 in terms of 𝑃 and 𝐴. We can do that by looking at our equation 𝑃 equals 𝐹 over 𝐴 and solving for 𝐹. We can multiply both sides of this equation by 𝐴. And then, we’ll have 𝐴 times 𝑃 equal to — well, times 𝐴 divided by 𝐴 cancels out, leaving us with 𝐹. 𝐴 times 𝑃 equals 𝐹. The force equals the area times the pressure. It’s also correct to say 𝐹 equals 𝑃 times 𝐴. The force could equal the pressure times the area.
And so we’re looking for an answer choice that either says 𝐹 equals 𝐴𝑃 or 𝐹 equals 𝑃𝐴. And for us, that’s option A. 𝐹 equals 𝑃𝐴.