Question

A fire hose 5 centimeters in diameter is used to fill a 225-liter bucket. If it takes 15 seconds to fill the bucket, what is the speed at ...

Answer 1

I believe you ask about speed at the end of the hose:

The volume of the bucket is 225 liters which is equal to 225 $dm^{3}$.
$V=225dm^{3}$
Hose's cross section can be counted with the typical circle's area formula (with diameter instead of radius, that's why you've got a fraction):
$A=3,14*\frac{d^{2}}{4}}=0,19625dm^{2}$

$225dm^{3}$ are filled within 15 second.

As the bucket is being filled you can say that it's volume is the volume of the water that flowed out of the hose, then:
$V=A*h$
The speed of the water can be counted with equation:
$v=\frac{h}{t}$
After extracting h from the volume's equation you get:
$v=\frac{V}{A*t}$
When you count the fraction you get the answer:
$v=76,43\frac{dm}{s}=0,7643\frac{m}{s}$