Sujet: Wheat/cone Nom: rachel Qui êtes-vous? étudiant wheat is poured through a chute at the rate of 10 cubic feet per minute and falls in a conical pile whose bottom radius is always half the altitude. how fast will the circumference of the base be increasing when the pile is 8 feet high? Hi Rachel, The volume of a conical pile is changing as wheat is being pored from the chute so you are probably going to need an expression for the volume of a cone. The volume of a cone is given by V = 1/3 π r2 h where r is the radius of the base and h is the height. In your situation you know that the radius is half the height so the volume expression can be changed to V = 2/3 π r3 You are asked how fast the circumference is changing so you are going to need an expression for the circumference of a circle. The circumference of a circle is given by C = 2 π r These are not static equations, they are dynamic. As you pour wheat onto the pile V changes so r changes which forces C to change. In other words V, r and C are all functions of time t. Differentiate both sides of both equations with respect to t. (Do it and then read on.) The first derivative equation has dV/dt on the left side and the variables on the right side are r and dr/dt. The second derivative equation has dC/dt on the left and the only variable on the right side is dr/dt. You are asked for dC/dt at a particular time, so from the second derivative equation, if you know dr/dt at this time you can find dC/dt. From the first derivative equation you know dV/dt = 10 cu ft per min and hence if you know r at the particular time of interest you can find dr/dt at this time. What is r at the time when h is 8 ft? Penny