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

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) (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 =
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 = = 60 hrs (vol = 0)
Therefore: t=60; v=0
:
Find the slope: m = = is the slope
:
An equation: V = t + 12566
:
You can illustrate this with a graph. V = vertical axis; t = horizontal axis

:
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 =
V = 6283 cu ft
:
Using the equation/graph
v = (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.
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