a hard math question for me...?

Question

hi guys...can you help me with my homeowrk, i've tried so many resources at home related to my homework but i can't figure out how to solve this one....

here it goes......

use the double integral to find the volume of a solid bounded by the coordinate planes and the surface x^1/2 + y^1/2 + z^1/2 = a^1/2........

can you help me out with this one.....

thanks a lot in advance..........

have a nice day.....

Answer 1

EDITED 3/11/07 I did work this out, and the integral is messy but not difficult. The answer is V=(a^3)/90. Contact me via answers e-mail if you would like to see the solution.


EDITED: 3/10/07

The area of a plane section of the volume parallel to the x,y plane and at location z is (note the surface intersects the x, y and z axes at x = a, y = a, and z = a):

..(√a-√z)^2
.......∫y(x,z)dx
......0

sum the areas of these sections over the z axis to get

a ..(√a-√z)^2
∫ ........ ∫y(x,z)dxdz
0.......0

where y(x,z) = [√a - √x - √z]^2

Answer 2

2sqrtx 2sqrty 2sqrtz 2sqrta