Answer :
The following conversion equivalents given: 1 gal = 231 in³ 1 ft = 12 in 1 min = 60 s, the rate in ft³/s, is closest to: b). 0.21.
To convert the rate of water delivery from gallons per minute (gal/min) to cubic feet per second (ft³/s), we need to use the given conversion equivalents.
First, let's convert gallons to cubic inches, and then cubic inches to cubic feet.
Given:
- [tex]\(1 \, \text{gal} = 231 \, \text{in}^3\)[/tex]
-[tex]\(1 \, \text{ft} = 12 \, \text{in}\)[/tex]
- [tex]\(1 \, \text{min} = 60 \, \text{s}\)[/tex]
So, to convert gallons to cubic feet:
[tex]\[ 1 \, \text{gal} = 231 \, \text{in}^3 \][/tex]
[tex]\[ 1 \, \text{gal} = \frac{231}{12^3} \, \text{ft}^3 \][/tex]
[tex]\[ 1 \, \text{gal} = \frac{231}{1728} \, \text{ft}^3 \][/tex]
[tex]\[ 1 \, \text{gal} \approx 0.13368 \, \text{ft}^3 \][/tex]
Now, let's convert gallons per minute to cubic feet per second:
[tex]\[ 95 \, \text{gal/min} \times \left(0.13368 \, \text{ft}^3/\text{gal}\right) \times \left(\frac{1 \, \text{min}}{60 \, \text{s}}\right) \][/tex]
[tex]\[ \approx 95 \times 0.13368 \times \frac{1}{60} \, \text{ft}^3/\text{s} \][/tex]
[tex]\[ \approx 0.21 \, \text{ft}^3/\text{s} \][/tex]
So, the correct answer is b) [tex]\(0.21 \, \text{ft}^3/\text{s}\).[/tex]
To convert the water flow from 95 gal/min to ft^3/s, first convert gallons to cubic feet using the conversion 1 gal = 0.13368 ft^3, then convert minutes to seconds. The calculation gives approximately 0.21 ft^3/s, which is answer choice b.
To determine the rate at which water flows through a pipe in cubic feet per second when given a rate in gallons per minute, we must use conversion factors to change the units from gallons to cubic feet and from minutes to seconds. Given the conversion equivalents: 1 gallon = 231 cubic inches and 1 cubic foot = 1728 cubic inches, we can start by converting gallons per minute to cubic feet per minute. Then, we convert from minutes to seconds to find the flow rate in cubic feet per second.
First, we convert 95 gallons per minute to cubic feet per minute using the equivalences provided:
- 1 gallon = 0.13368 cubic feet (from 1 gallon = 231 cubic inches and 1 cubic foot = 1728 cubic inches).
So, 95 gallons per minute * 0.13368 cubic feet/gallon gives us the rate in cubic feet per minute:
95 * 0.13368 = 12.6996 cubic feet/minute.
Since there are 60 seconds in a minute, to convert to cubic feet per second, we divide the previous result by 60:
12.6996 cubic feet/minute
60 seconds/minute = 0.21166 cubic feet/second.
The rate of water flow through the pipe is therefore approximately 0.21 cubic feet per second, matching choice b.
