# Homework Help: Semi-circle cross section volume

1. Jun 15, 2011

### sy7ar

1. The problem statement, all variables and given/known data

base of a solid is bounded by y=$\sqrt{x}$, the x-axis, and x=9. each cross-section perpendicular to the x-axis is a semi-circle. find the volume of the solid

2. Relevant equations

3. The attempt at a solution
I found the answer to be 81$\pi$/16 by the following steps:
A(semicircle)=0.5pir^2=(pi/8)*d^2 (d=diameter), and d=y=sqrt(x), so A=(pi/8)*x
integrate (pi/8)*x from 0 to 9 (pi*9^2 /16), I get the answer as 81pi/16

BUT the answer provided by my book is 81pi/8, did I miss something? I'm so confused and please help.

Last edited: Jun 15, 2011
2. Jun 15, 2011

### Dick

I agree with you. Maybe we are both missing something, but I can't think what it might be.

3. Jun 15, 2011

### LCKurtz

I agree with you both.

4. Jun 15, 2011

### sy7ar

i guess the answer on my book is wrong then. I really cant think of any other ways

5. Jun 16, 2011

### LCKurtz

The book solution apparently calculated the volume assuming the cross section was a circle instead of a semi-circle.

6. Jun 16, 2011

### sy7ar

ya, that's what I think too. The thing is, my book's never wrong before (for several times I doubted its answers and it turned out it's always correct), and this is the last question for the last unit. Hopefully it's just a decoy this time hehe.