Question

How long will it take to fill a cylinder-shaped vat (with radius of 22.8 ft and depth of 20.2 ft) with a certain liquid (d=0.630 g/ml) if it is spilling out of the hose at 11080.0 g/s?

Answer 1

The time to fill a cylinder-shaped vat can be calculated by first finding its volume, converting the volume to milliliters, and then dividing by the flow rate, taking into account the density of the liquid to convert grams to milliliters.

Step-by-step explanation:

The question involves calculating the time it takes to fill a cylinder-shaped vat with a liquid when the rate of flow from a hose is given. To find the time required, we'll first need to calculate the volume of the cylinder using the formula
`V = \pi r^2h`, where V is the volume, r is the radius, and h is the height (or depth) of the cylinder.

After calculating the volume in cubic feet, we convert it to milliliters (mL), understanding that 1 cubic foot equals 28316.8 mL. Then, we calculate the time by dividing the total volume in milliliters by the flow rate, which is given in grams per second.

Since the density of the liquid (d) is provided, we can convert grams to milliliters using the density formula d = m/V, where m is mass in grams and V is volume in milliliters.