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

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- Sep 26th 2007, 09:32 AM^_^Engineer_Adam^_^Volume problems/ Integration
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 - Sep 26th 2007, 11:22 AMticbol
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.