Applications of integration - volume of volcanic ash

[Anabelle37]

Homework Statement

After a volcanic eruption, the ash gradually falls to the ground euqally in all directions. the depth of the ash diminishes with the distance from the volcano such that at a distance r metres the depth is exp(-r^2). find the total volume of ash falling within 1 km of the volcano.

The Attempt at a Solution

We've been doing solid revolutions in class for applications of integration. I tried to do this question by partitioning the y-axis so i could revolve aroung the y-axis to form a volume.
I called the radius exp(-r^2) and therefore my volume of my disc is pi*exp(-2r^2)*Delta(y). Then i realized that I couldn't integrate it from r=0 to r=1000 as my partition was for y not x. but partitioning x wouldn't seem correct. So now I'm completely stuck!

Any pointers would be great!
Is there another way to do it?

Thanks

 

[tiny-tim]

Hi Anabelle!

(have a pi: π and a delta: ∆ and try using the X² icon just above the Reply box )

erm … there are coordinates other than x and y !

try using r ​