Torricelli's Law (Seperable DE Application)

[PsychonautQQ]

Homework Statement

A spherical tank of radius 4(ft) is full of gasoline when a circular bottom hole with radius 1 in. is opened. How long will be required for all the gasoline to drain from the tank?

Homework Equations

dVolume/dTime = -a(2gy)^(1/2)

The Attempt at a Solution

Right now I'm trying to find an equation to express the cross sectional area of the sphere in terms of y. The answer solution manual I am looking out says that A(y) = ∏(4^2 - (4-y)^2). However, I don't see how this can be correct as that would mean the cross section area when y=4 is equal to ∏*16, which is obviously false, because the top of a sphere should have cross sectional area of 0. It works when you enter 0 in for y however. Help?

 

[pasmith]

Homework Statement

A spherical tank of radius 4(ft) is full of gasoline when a circular bottom hole with radius 1 in. is opened. How long will be required for all the gasoline to drain from the tank?

Homework Equations

dVolume/dTime = -a(2gy)^(1/2)

The Attempt at a Solution

Right now I'm trying to find an equation to express the cross sectional area of the sphere in terms of y. The answer solution manual I am looking out says that A(y) = ∏(4^2 - (4-y)^2). However, I don't see how this can be correct as that would mean the cross section area when y=4 is equal to ∏*16, which is obviously false, because the top of a sphere should have cross sectional area of 0. It works when you enter 0 in for y however. Help?

The sphere has radius 4, so if its bottom is at $y = 0$ then its center is at $y = 4$ and its top is at $y = 8$.