# Homework Help: Help with calc

1. Jan 9, 2005

The base od a solid is a region in the 1st quadrant bounded by the x-axis, y-axis and the line x+2y=8. If cross sections of the solidperpendicular to the x-axis are semicircles, what is the volume of the solid?

How come the answer isnt just the intgegral from 0-8 of 1/2pi(4-x/2)^2

2. Jan 9, 2005

### learningphysics

That's what it looks like to me. Is it the wrong answer?

3. Jan 9, 2005

yea according to the answer key its wrong

4. Jan 9, 2005

choices are
a. 12.566 b. 14.661 c. 16.755 d 67.021 e 134.041

i keep ending up with choice d but the answer key says its choice c

5. Jan 9, 2005

### learningphysics

Oh I see now. I misunderstood the problem. I did it by finding the solid after rotating about the x-axis and integrating... But the cross section of this solid is the circle whose diameter is from y=0 to y=4-x/2. We were thinking the cross section was a circle with diameter from y=-(4-x/2) to y=4-x/2. But if we make the radius (4-x/2)/2, then we get the right answer.

0-8 of 1/2pi[1/2(4-x/2)]^2 is correct.

6. Jan 9, 2005