# Torricelli's Law (Seperable DE Application)

1. Jan 28, 2014

### PsychonautQQ

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

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

3. 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?

2. Jan 28, 2014

### pasmith

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 $y = 8$.