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.
(a) Let h represent the depth of the water, as shown.
Then h is the altitude of an equilateral triangle, and the base .
The volume of water is
Now , and it is given that . Thus, when h = 4,
(b) Let x represent the length of one of the sides, as shown. The bases of
