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 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?

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)posted by Steve
Respond to this Question
Similar Questions

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 
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 
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.] 
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? the water in tank is transferred into small cylindrical tanks each of diamter 70cm and height 40 
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? 
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? Thank You! :) 
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 
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= ? a)50 b)100 c)200 d)300 e)400 small tank volume: 
WORD PROBLEM HELP
Mr. Wu needs to buy a right cylindrical fish tank that holds between 75 and 100 cubic meters of water. Using only these numbers: 2,3,4,5,6, and 7, identify a radius and a height for three different tanks that would fit Mr.Wu"s 
MATH WORD PROBLEM HELP PLEASE
Mr. Wu needs to buy a right cylindrical fish tank that holds between 75 and 100 cubic meters of water. Using only these numbers: 2,3,4,5,6, and 7, identify a radius and a height for three different tanks that would fit Mr.Wu"s