Main Question or Discussion Point
Alright, so I've got this volume problem and it seemed really easy, only my answer is off, if only by a little bit. The problem is this: There is a tunnel, with a cross-section in the shape of a parabola, that is 5 meters wide and 10 meters high (I got the equation to be y=-1.6x^2 + 10). It takes someone driving 50 miles per hour 3 minutes to get through the tunnel (2.5 miles or 4023.36 meters). What is the volume of the tunnel? Well, i took the integral of y=-1.6x^2 + 10 from -2.5 to 2.5 and got 100/3. then i multiplied that by 4023.36 and got 134112 cubic meters. But my teachre says this is wrong. I used a different conversion, where the 2.5 miles equalled 4022.857 meters, and she said this was closer. Am i just off with my integration, or am I just crazy?