Im reviewing for my calculus final exam and I was just going through some problems that I didnt understand and never got back to them. Im trying to solve this one out and I cant get it right.
A swimming pool is 22 ft wide, 60 ft long, 2 ft deepat the shallow end, and 10 ft deep at its deepest point. If the pool is being filled with water at a rate of 0.8ft^3/min, how fast is the water level rising when the depth at the deepest point is 7 ft??
I keep getting .00115ft/min and i know thats not the right answer.
Can some one give me a hand?
My apologies I repeated my calculation and got 0.00069264069 as well. Rounding error the first time:
Let the height = h. Let S be the length of the slope of the pool as the depth changes from 2 feet to 10 feet. Then Cos(theta) = 8/60
theta = Cos(^-1) (8/60)
= 82.33774434 * (let * be degrees) here on referred to as A
Thus Cos (A) = h/S
Let the length of the triangular prism (where the whole triangular prism has dimensions: Length 60 feet, height 8 feet, width 22 feet, slope 60.5309838 feet)
(SQUARE ROOT OF: ((h^2)/cos^2 (A) - h^2)) gives LENGTH L. (Pythagorus' theorem)
Thus volume of triangular prism given by:
V = (1/2)(h)((SQUARE ROOT OF: ((h^2)/cos^2 (A) - h^2)))22
= 11(h^2)((SQUARE ROOT OF: (1- cos^2 (A))/cos^2 (A)))
dV/dt = .8
dh/dt = (dh/dV)(dV/dt)
= (dh/dV) .8
dV/dh = 22h((SQUARE ROOT OF: (1- cos^2 (A))/cos^2 (A)))
dh/dV = 1/22h((SQUARE ROOT OF: (1- cos^2 (A))/cos^2 (A)))
dh/dt = (.8)1/22h((SQUARE ROOT OF: (1- cos^2 (A))/cos^2 (A)))
where A = 82.33774434 * (let * be degrees)
Let h = 7
dh/dt = 0.00069264069
Hello, ((ECHO))!
I get the same answer is behemoth and Jhevon . . .
A swimming pool is 22 ft wide and 60 ft long.
It is 2 ft deep at the shallow end, and 10 ft deep at the other end.
If the pool is being filled with water at a rate of 0.8 ft³/min,
how fast is the water level rising when the depth at the deepest point is 7 ft?Code:60 - * - - - - - - - - - - - - - - - - - - - - * : | | 2 | | 2 : | 60 | - A + - - - - - - - - - - - - - - - - - - - - * B : | * : | x * : C +-----------------------* D 8 |:::::::::::::::::* : |h :::::::::* : |:::::* - E *
Since , we have: . .[1]
. . Hence: . . [2]
The volume of water is: .
. . Then: . . [3]
When , [1] gives us: .
Substitute into [3]: .
Hence: .
Therefore: . ft/min.