Question

I was under the impression this one could only be solved using the volume? Why is it saying to use area? Help!

Answer 1

Water is flowing out of a garden hose at a rate of 10 gallons per minute into a circular swimming pool that has a diameter of 16 ft. How fast is the water rising in the pool in inches per minute? (Hint: The area of a circle is A=pi r^2)

Answer 2

I don't see how this could be solved using the area of a circle. I was almost thinking it had to be a rate of change using the derivative. But this is basic Math 070.

Answer 3

well in this we dont know the depth of the swimming pool so we need to use the area

Answer 4

means in one minute 10 gallons of water fall in the pool
let depth of pool up to which it is filled by 10 gallon = x ft

Answer 5

10 gallon /minute = (area of circle *x)/minute

Answer 6

10=pi*16^2*x
x=10/(pi*16^2)

Answer 7

this depth of pool filled in one minute
so rate of fill = x/minute

Answer 8

That doesn't make sense to me at all. I really don't understand what you just did.

Answer 9

@amistre64

Answer 10

got it

Answer 11

WHY did they say to use the area?!!!!! I don't get that at all! How does it relate?

Answer 12

the rate at which a volume is changing is directly related to area

Answer 13

how?

Answer 14

area is for a flat, 2 dimensional figure. This is a 3d problem, in my eyes.

Answer 15

also, how do we find the volume of a cylindar?

Answer 16

volume equals pi times the rate squared times the height of the cylinder.

Answer 17

pi times the radius squared

Answer 18

or Base area ... times height

Answer 19

still not making sense.

Answer 20

we know 10 gallons a minute is coming in, what is that in cubic inches per minute in order to get the dimensions the same

Answer 21

2310 in cubic inches.

Answer 22

the wolf says 1 gallon is equal to 231 cubic inches

Answer 23

10 galons is therefore 2310 cubicinches yes

Answer 24

so we know the volume per minute that is coming into the pool, what is the base area of the pool

Answer 25

64pi

Answer 26

201.06

Answer 27

hmm, lets convert 16 feet into inches

Answer 28

area is in units squared. Volume is cubic.

Answer 29

192 inches.

Answer 30

pi (r in)^2 * (h in) = k (in)^3

Answer 31

well, 8 feet radius, is 96 inches

Answer 32

in this if we go up we will consider it as water is travelling up with what speed

Answer 33

what the heck is that k up above, @amistre64

Answer 34

like water level is rising 2 ft /minute 3 ft /minute

Answer 35

so

96 inches ^2 * pi * h inches = 2310 inches^3

96 * pi * h inches^3 = 2310 inches^3

solve for h

Answer 36

so we consider that water poured in it equal to
= areal * height

Answer 37

pi*r^2 * height

Answer 38

ugh, 96 is squared as well since its the r lol

Answer 39

you r right @amistre64

Answer 40

96^2 * pi * h inches^3 = 2310 inches^3

does this make sense?

Answer 41

no this doesn't make sense to me AT ALLLLLLLLLLLLLLLL

Answer 42

lookkk

Answer 43

where did you get the cube on the h?

Answer 44

tell me the volume of pool filled ??

Answer 45

the conversions are the hardest part, the rest is pretty basic

Answer 46

@IMStuck i can try if u will follow

Answer 47

if u had area and height can u calculate volume ???

Answer 48

Oh1!!!!!!!!!!!!!!!!! yes I can do that!

Answer 49

The pi r^2 part of volume is the same as the area of the circle. I see that.

Answer 50

but here height = rise in water level

Answer 51

yeah

Answer 52

\[Basearea(height)=volume\]
\[pi~(r)^2(h)=(10~gallons)\]
\[pi~(8~ft)^2(h)=2310~in^3\]
\[pi~(96~in)^2(h)=2310~in^3\]

Answer 53

initially water level =0

Answer 54

let after puting 10 gallon
now water level = x feet

Answer 55

so now water rose from 0 to x feet in one minute

Answer 56

ok, the second step up there is where I'm confused, @amistre64 Where you said this:
pi r^2 h = 10 gallons.

Answer 57

guys don't leave me here!

Answer 58

why? we are told 10 gallons is the volume per minute, and we have established the p r^2 h is the volume of a cylindar equate the 2 of them

Answer 59

the rest is conversion to inches to determine the required solution in inches per minute

Answer 60

but the volume is not equal to 10 gallons per minute....it's changing constantly. It is never JUST 10 gallons so I don't see how you can equate them.

Answer 61

'Water is flowing out of a garden hose at a rate of 10 gallons per minute'

use the information provided instead of making up a different problem

Answer 62

in accounting classes i was real good at solving the problem that i made up instead of the problem that was being asked :)

Answer 63

lol. I know I'm making it harder than it should be. I still don't get the "equate them" thing.

Answer 64

what is the volume of a cylindar? what is the volume that is coming from the hose?

volume of cylindar = volume from hose

Answer 65

This is what I have so far... can you help me take it from there?