An oil tank in the shape of a sphere has a diameter of 60ft. How much oil does the tank contain if the depth of the oil is 25 ft?
x^2 + y^2 = 30
25x = depth
$\displaystyle \pi \int_{0}^{30} (\sqrt{30 - x^2})^2 dx$
help
If the diameter is 60ft, then the radius is 30ft, so the equation of the circle, if (0,0) is the origin, is
x^2 +y^2 = 30^2
x^2 +y^2 = 900 ------------(i)
dV is a disc of radius x, and height dy.
dV = pi(x^2)*dy
dV = pi(900 -y^2)dy
dy goes from y = -30 to y = -5
So,
V = (pi)INT.(-30 to -5)[900 -y^2]dy
V = 42,542.4 cu.ft. -------------answer.