precalculus- A cylindrical tank with a cross-sectional area of 100cm^2 is filled to a depth of 100cm with water. At time t=0sec. a drain at the bottom of tank w/ an area of 10cm^2 is opened, allowing water to flow out of the tank. The depth of the water at time t≥0, is d(t)=(10-2.2t)^2.

a) what is the initial volume of water in the tank?
-I'm not quite sure how to find volume out of depth..
b) what is the depth of the water at time t=1 sec.? What is the volume of water at this time?
- d(1)=(10-2.2*1)^2=60.84cm, same as above, not sure how to figure out the volume out of depth.

Question

precalculus- A cylindrical tank with a cross-sectional area of 100cm^2 is filled to a depth of 100cm with water. At time t=0sec. a drain at the bottom of tank w/ an area of 10cm^2 is opened, allowing water to flow out of the tank. The depth of the water at time t≥0, is d(t)=(10-2.2t)^2.

a) what is the initial volume of water in the tank?
-I'm not quite sure how to find volume out of depth..
b) what is the depth of the water at time t=1 sec.? What is the volume of water at this time?
- d(1)=(10-2.2*1)^2=60.84cm, same as above, not sure how to figure out the volume out of depth.

phi · Answer

see http://www.mathsteacher.com.au/year9/ch14_measurement/18_cylinder/cylinder.htm V= area of the base times height

anonymous · Answer

Phi, um cant you just multiply given area and the depth since area gives you 2dimensions you need for the volume and depth will give the third? which is 100cm^2 * 100cm = 10000cm^3??

anonymous · Answer

But that is exactly what you do when you take a rectangle and multiply the sides to get the area inside. 5cm * 4cm = 20cm^2

anonymous · Answer

@pitamar  yeah.. Now i think about it , it is.

anonymous · Answer

Well, I was about to write more detailed answer, but seems you get it pretty much. =]

phi · Answer

Phi, um cant you just multiply given area and the depth since area gives you 2dimensions you need for the volume and depth will give the third? which is 100cm^2 * 100cm = 10000cm^3??

Yes,  that is the volume=  area of the base * height

anonymous · Answer

@pitamar @phi 
So am i right on the (a)?  And for (b), do i use new depth at time t=1 to multiply with the given area to find the volume at that time? And please, pitamar give me a detailed answer, I'm still quite not sure where i'm heading to.

phi · Answer

yes, depth at t=1 is correct

volume=  cross-sectional area  * height

phi · Answer

see http://www.mathsisfun.com/geometry/cross-sections.html scroll down to picture of a cylinder

e.mccormick · Answer

|dw:1381619679771:dw|

anonymous · Answer

@phi Ohhh, now I get it completely, thank you so much Phi! :D

anonymous · Answer

@e.mccormick  Thank you for very nice drawing, it helps me to get a clear idea :D

e.mccormick · Answer

yah, I like images too!  Hehe.

anonymous · Answer

@e.mccormick  yeah, I need to draw every time i have a word problem :)

e.mccormick · Answer

That is a very good tactic!  Even a simple, no to scale sketch can help you see what needs to go where, what you know, and what you need to find along the way to get to the answer.

anonymous · Answer

@e.mccormick  Indeed! But, sometimes the drawing tactic doesn't work... it makes me a blank head...