Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the water drains out at a rate of 1/2 cubic feet per second. Note: The volume of a cylinder is V=(pi)(r^2)(h).
A. Find the volume, V, of the water remaining in the small tank as a function of time.
B. How long does it take for the small tank to completely empty?
C. Let z be the depth of the water in the large tank, which is initially empty. Compute dz/dt.
D. What fraction of the total amount of water is in the large tank at time t=6?
1 answer
The large cylinder has a cross-section 4 times that of the smaller one, so its water level rises 1/4 as fast as it falls in the smaller one.
2 answers