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).

Question

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?

Answer 1

A) V(t) = π*4^2*6 - 1/2 t
B) solve for t in V=0
C) z = (1/2 t) / (π*8^2) so dz/dt = 1/(2π*8^2) ft/s
D) V(6)/V(0)