Explained: AP Calculus AB/BC 2021 FRQ #3

AP Calculus AB free response question #3.

A company designs spinning toys using the family of functions y = cx*sqrt(4-x^2) , where c is a positive constant. The figure above shows the region in the first quadrant bounded by the x-axis and the graph of y = cx*sqrt(4-x^2) , for some c. Each spinning toy is in the shape of the solid generated when such a region is revolved about the x-axis. Both x and y are measured in inches.

0:00 Intro
0:05 Part A
3:15 Part B
5:31 Part C
7:23 Point Prediction

[aartigaraye]

How did you know they were asking for the max value in 3b.. or how did it click to your brain that by solving for critical numbers you can get the value for x