Semi-circle cross section volume

[sy7ar]

Homework Statement

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

Homework Equations

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.

 

[Dick]

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

 

[LCKurtz]

I agree with you both.

 

[sy7ar]

i guess the answer on my book is wrong then. I really can't think of any other ways

 

[LCKurtz]

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

 

[sy7ar]

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

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.