How long will it take to fill a cube-shaped vat with edge length 18.2 ft with a certain liquid (d=0.890 g/mL) if it is spilling out of the hose at 11046.9 g/s? (1.00 in = 2.54E0 cm)

Question

How long will it take to fill a cube-shaped vat with edge length 18.2 ft with a certain liquid (d=0.890 g/mL) if it is spilling out of the hose at 11046.9 g/s?

(1.00 in = 2.54E0 cm)

4.76×10^-9 hr

0.0617 hr

3.82 hr

1.06×10⁶ hr

1.59×10⁷ hr

Answer 1

First, let's find the volume of the cube, in cm³. Volume of cube = edge cubed = a³

The edge is 18.2 ft. Converting this to cm, we have 18.2 ft x 12 inches/ft x 2.54 cm/inch = 554.74 cm

Area = 554.74cm³ = 1.71x10⁸ cm³

Now converting cm3 to gallons we have 1.71x10⁸ cm³ x 1 gallon/3.785x10³ cm³ = 45,178 gallons

Finding time to fill the cube at a rate of 11046.9 g/sec we have 45,178 g x 1 sec/11046.9 g = 4.09 sec

Converting to hours we have 4.09 sec x 1 hour/60 sec = 0.0682 hrs

So answer would be (B) 0.0617 hours (rounding differences)