Related Rates - Cylindrical Pools

[DrummingAtom]

Homework Statement

2 Cylindrical pools are filled simultaneously at the same rate, 1m³/min. The smaller pool has radius 5m and the water level rises at a rate of 0.5m/min. The larger pool has a radius 8m. How fast is the water level rising in the larger pool?

Homework Equations

V = pi(r²)h

The Attempt at a Solution

I took the derivative of V with respect to h and got:

dV/dt = pi(r²)(dh/dt)

Which dV/dt = 1 and then I just solve for dh/dt. But, if I'm doing this right, the smaller pool should yield the same answer and it doesn't. Because for the smaller pool I would have:

1/pi(5²) = dh/dt and this doesn't equal 0.5m³/min.

Thanks for any help.

 

[Mark44]

Homework Statement

2 Cylindrical pools are filled simultaneously at the same rate, 1m³/min. The smaller pool has radius 5m and the water level rises at a rate of 0.5m/min. The larger pool has a radius 8m. How fast is the water level rising in the larger pool?

Homework Equations

V = pi(r²)h

The Attempt at a Solution

I took the derivative of V with respect to h and got:

dV/dt = pi(r²)(dh/dt)

Which dV/dt = 1 and then I just solve for dh/dt. But, if I'm doing this right, the smaller pool should yield the same answer and it doesn't. Because for the smaller pool I would have:

1/pi(5²) = dh/dt and this doesn't equal 0.5m³/min.

Thanks for any help.

I partly agree with you. As stated, the problem doesn't make sense as far as the small pool is concerned. If the pool is being filled at a rate of 1 m^3/min, the rate of change of the water height is 1/(25pi) m/min, which is at odds with the given information.

Where you say that the water in both pools should rise at the same rate, I disagree. Given that both pools are being filled at a rate of 1 m^3/min, the water level in the smaller pool will rise more quickly than it will in the larger pool.