SOLUTION: My question is on solving a word problem. I dont if you can help but this is the problem: aA vertical cylindrical storage tank, with diameter 20 feet, is filled with oil to a d

Algebra ->  Rate-of-work-word-problems -> SOLUTION: My question is on solving a word problem. I dont if you can help but this is the problem: aA vertical cylindrical storage tank, with diameter 20 feet, is filled with oil to a d      Log On


   

Question 160373: My question is on solving a word problem. I dont if you can help but this is the problem:
aA vertical cylindrical storage tank, with diameter 20 feet, is filled with oil to a depth of 40 feet. Sometime later, the oil is drained, decreasing the deptht a rate of 8 inches per hour. Write an equation for the volume of oil (ft^3) remaining in the tank t hours later as a function of t. Draw a geometrically correct sketch, supporting your solution.
The only thing i can pull out of this problem is that the volume of a cylinder is V = πr^2h. If you could help it would be greatly appreciated.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A vertical cylindrical storage tank, with diameter 20 feet, is filled with oil
to a depth of 40 feet. Sometime later, the oil is drained, decreasing the
depth a rate of 8 inches per hour. Write an equation for the volume of oil
(ft^3) remaining in the tank t hours later as a function of t.
Draw a geometrically correct sketch, supporting your solution.
:
This is a linear equation so we can find the slope using the time/volume
:
Find the volume at 40 ft, (radius = 10 ft)
V = pi%2A10%5E2%2A40
V = 12566 cu ft (rounded to nearest cu ft)
:
Therefore: t=0; v=12566
:
Find out how many hours to empty the tank
:
At 8 in/hr how long to lower it 40 ft?
t = %28%2840%2A12%29%29%2F8 = 60 hrs (vol = 0)
Therefore: t=60; v=0
:
Find the slope: m = %28%280+-+12566%29%29%2F%28%2860-0%29%29 = -12566%2F60 is the slope
:
An equation: V = -12566%2F60t + 12566
:
You can illustrate this with a graph. V = vertical axis; t = horizontal axis
+graph%28+300%2C+200%2C+-20%2C+80%2C+-5000%2C+15000%2C+%28-12566%2F60%29x%2B12566%29+
:
You can prove this:
t = 30 hr
At 30 hrs the depth would be 30*8" = 240" = 20 feet (40-20)
Find the volume at 20ft
V = pi%2A10%5E2%2A20
V = 6283 cu ft
:
Using the equation/graph
v = -12566%2F60(30) + 12566
v = 6283 cu ft
:
Did this sense to you? I am not sure what kind of sketch they have in mind, I'll
leave that up to you.