Chapter 3.4, Problem 34E

Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always four times its height. Suppose the height of the pile increases at a rate of 1 cm/s when the pile is 13 cm high. At what rate is the sand leaving the bin at that instant? Let V and h be the volume and height of the cone, respectively. Write an equation that relates V and h and does not include the radius of the cone. (Type an exact answer, using n as needed.) Differentiate both sides of the equation with respect to t. dV dh %3D dt dt (Type an exact answer, using n as needed.) The sand is leaving the bin at a rate of (Type an exact answer, using a as needed.)

Poiseuille's Law states that the volume, V, of blood flowing through an artery in a unit of time at a fixed pressure is directly proportional to the fourth power of the radius of the arter That is, V = kr“, where r is the radius of the artery. If the radius is increased by about 4 %, by about how much will the volume of blood flowing through the artery increase? 16 % By about how much must the radius of the artery be increased to achieve a 50 % increase in the volume of blood flowing through the artery? % Note: enter an answer accurate to 4 decimal places.

Show the solution and draw the figure. The height and base radius of a right circular cylinder are 20 cm and 8 cm respectively. If the height decreases at the rate of 3 cm/s and its base radius increases at the rate of 2 cm/s, at what rate is its volume changing? a. 448 pi b.428 pi