Problem
Gas is escaping from a spherical balloon at a constant rate of 2 ft3/min. How fast, in ft2/min, is the outer surface area of the balloon shrinking when the radius is 12 ft?
| A. 1/2 | C. 1/3 |
| B. 1/5 | D. 1/4 |
Problem
A meteorologist is inflating a spherical balloon with a helium gas. If the radius of a balloon is changing at a rate of 1.5 cm/sec., express the volume V of the balloon as a function of time t (in seconds). Hint: Use composite function relationship Vsphere = 4/3 πr3 as a function of x (radius), and x (radius) as a function of t (time).
| A. V(t) = 5/2 πt3 | C. V(t) = 9/2 πt3 |
| B. V(t) = 7/2 πt3 | D. V(t) = 3/2 πt3 |
Problem
A conveyor is dispersing sands which forms into a conical pile whose height is approximately 4/3 of its base radius. Determine how fast the volume of the conical sand is changing when the radius of the base is 3 feet, if the rate of change of the radius is 3 inches per minute.
| A. 2π ft/min | C. 3π ft/min |
| B. 4π ft/min | D. 5π ft/min |
Problem
Gas is escaping from a spherical balloon at the rate of 2 cm3/min. Find the rate at which the surface area is decreasing, in cm2/min, when the radius is 8 cm..
Problem 52
A car drives south at 20 mi/hr. Another car, starting from the same point at the same time and traveling 40 mi/hr, goes east for 30 minutes then turns north. Find the rate of rotation of the line joining the cars (a) 1 hour after the start; (b) at the time the second car makes its turn.
Graph of the Function y = f(x)
The graph of a function y = f(x) may be plotted using Differential Calculus. Consider the graph shown below.
As x increases, the curve rises if the slope is positive, as of arc AB; it falls if the slope is negative, as of arc BC.
