- The figure above shows an elliptical cross section of the tank. Its equation is
(a) The volume of the tank, using disks, is where the ellipse’s symmetry about the x-
axis has been exploited. The equation of the ellipse is equivalent to x^2 = 6.25(100 − y^2 ), so
Use the calculator to evaluate this integral, storing the answer as V to have it available for part
(b).
The capacity of the tank is 7.48V, or 196,000 gal of water, rounded to the nearest 1000 gal.
(b) Let k be the y-coordinate of the water level when the tank is one-fourth full. Then
and the depth of the water is k + 10.
