Teen disappointed by Shrinking Pizza
The rates of changes of two quantities are given, and the problem asks for the rate of change of a third quantity that is related to the given quantities, so we can immediately tell that this is clearly a related rates problem.
For this problem we are assuming that the pizza is a perfect cylinder, so the equation for the volume of the cylinder is V = pi*r^2. Based on information given in the problem, we can also determine dr/dt and dh/dt.
Solve for the radius and height of the pizza after 5 minutes.
Using the product rule, find the derivative of the volume equations and plug in the other values dr/dt, dh/dt, h, and r to calculate dv/dt. The final answer is that the pizza's volume is decreasing at a rate of -3.45 cubic inches per minute.
No comments:
Post a Comment