# CALCULUS

posted by Anonymous

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. Steve

the small tank has a volume of 96π ft^3

its depth decreases at a rate of (1/2)/(16π) = 1/(32π) ft/s

So,

A: v(t) = 96π - 1/2 t
B: duh
C: the large tank's area is 4 times as big, so its depth increases 1/4 as fast, or 1/8 ft/s.
D: 6/(192π)

## Similar Questions

1. ### math

two cylindrical tanks have the same height, but the radius of one tank equals the diameter of the other. if the volume of the larger is k% more than the volume of the smaller, k= ?
2. ### algebra

You are standing 14 feet from the edge of a cylindrical water tank and 26 feet from a point of tangency. The tank is 10 feet tall. What is the volume of the tank in cubic feet?
3. ### Calculus

A cylindrical water tank has a radius of 2 feet and a height of 6.0 feet. Compute the work done to pump the water out of a filled tank through the top. [The density of water is 62.4 lbs/ft3.]
4. ### math

A cylindrical tank has a radius of 15 ft. and a height of 45 ft. How many cubic feet of water can the tank hold?
5. ### Algebra

a cylindrical water tank has a volume of 20π cubic feet . the height of the tank is 1 foot more than 2 times of its radius . find the radius and height of the tank
6. ### Calculus

Water is running into an open conical tank at the rate of 9 cubic feet per minute. The tank is standing inverted, and has a height of 10 feet and a base diameter of 10 feet. At what rate is the radius of the water in the tank increasing …
7. ### calculus

water is being siphoned from a cylindrical tank of radius 10m into a rectangular tank whose base measures 20m by 15m. if the depth of the water in the cylindrical tank in decreasing at a rate of 2m/s, at what rate is the depth of the …
8. ### Calculus

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 …
9. ### Maths

a rectangular tank measured internally is 2.5m long,1.5m wide and 0.8m high. how many litres of water are needed to fill the tank?
10. ### Calculus

Water is flowing into a vertical cylindrical tank at the rate of 24 cu. ft. per minute. If the radius of the tank is 4 feet, how fast is the surface rising?

More Similar Questions