Question

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

(x^2/3600)+(y^2/1600)= 1
The cross sections perpendicular to the ground and parallel to the y-axis are squares. Find the total volume of the pool.

Answer 1

Integrating along x, the area of each cross-section is (2y)^2 = 4y^2.

The equation of the ellipse means

4y^2 = 6400 - 6400x^2/3600 = 6400 - 8/9 x^2

v = ∫[-60,60] 6400 - 8/9 x^2 dx
let 'er rip.

Answer 2

266666.66667