2004 AP Calculus Free Response Question 2b --> Disks/Washers

[Baron]

I need help on the 2004 AP Calculus Free Response question 2B

Here's the answer key ... scroll down for question 2B.
http://apcentral.collegeboard.com/apc/public/repository/ap04_sg_calculus_ab_36998.pdf

The question wants me to find the volume of the shaded region when it is revolved around the line y = 2. To do this using the washer method, I need to find the outer radius and inner radius.

I understand why the inner radius = 2 - f(x) but I thought the outer radius = 2 + g(x) because that gives the distance from the function y=g(x) to the line y=2. Instead according to the answer key, the outer radius = 2 - g(x)

How come? I thought I understood the washer method but this question just confuses me.

 

[tkhunny]

Please rethink.

Take h(x) = 2

Which expression suggests the distance from y = 2 to h(x),

2 - h(x) or 2 + h(x)

Given your g(x), ponder 2 - (-2) = 2 + 2 = 4, vs 2 + (-2) = 2 - 2 = 0

Points: You knew the distance would be positive.
Points: You knew the values for g(x) were negative over the specified Domain.
Points: You knew the distance was the sum of two parts, 1) The distance from g(x) to the x-axis, then 2) Two more than that.
Whoops: You were so close. You wandered off when you forgot that "the distance from g(x) to the x-axis" is NOT g(x). It is |g(x)| or -g(x) over the specified Domain.