1. ## Volume

As viewed from above, a swimming pool has the shape of the ellipse given by

The cross sections perpendicular to the ground and parallel to the -axis are squares. Find the total volume of the pool.

2. Originally Posted by amiv4
As viewed from above, a swimming pool has the shape of the ellipse given by

The cross sections perpendicular to the ground and parallel to the -axis are squares. Find the total volume of the pool.
note that the the curve is given by $y = \pm \sqrt{2500 - \frac {25x^2}{49}}$

the plus part gives the curve above the x-axis, the minus part gives the curve below the x-axis.

recall, the volume is given by

$V = \int_a^b A(x)~dx$

where $A(x)$ is the cross-sectional area.

note that here, $A(x)$ is given by the formula for a square, where the side length is given by the difference between the two functions.

3. so is A(x) = x^2
im confused on that part

4. Originally Posted by amiv4
so is A(x) = x^2
im confused on that part
i told you, the height of the square is the difference between the two functions. draw any vertical line in the ellipse that connects the top to the bottom. the length of that line is the side length of the square at that point. it's length is given by the difference of the functions

5. so A(x) = (sqrt(2500-25x^2/49)-(-sqrt(2500-25x^2/49)))^2

6. Originally Posted by amiv4
so A(x) = (sqrt(2500-25x^2/49)-(-sqrt(2500-25x^2/49)))^2
yes, but of course you can simplify that a lot. who'd want to integrate that thing?!

7. is it integrated from 0 to 1

8. Originally Posted by amiv4
is it integrated from 0 to 1
no

look at the graph, or better yet, solve for the x-intercepts of your functions. you realize that those will be your limits of integration, right?

9. so it would be from -70 to 70

10. Originally Posted by amiv4
so it would be from -70 to 70
yes

11. k well i put that in my calculator and got 933333.3333 and that isnt right so idk what else im not doing. Did u get something close to that

12. Originally Posted by amiv4
k well i put that in my calculator and got 933333.3333 and that isnt right so idk what else im not doing. Did u get something close to that
that is what i got

we can check to see if we missed something

13. oh ok i just forgot one of the 3's when i put it in. so it works now. Thanks