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3 years ago

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Water flows into a swimming pool at the rate of 8.0 gal/min. The pool is 16 ft wide, 32 ft long and 8.0 ft deep. How long does i

t take to fill in hours? (1 U.S. gallon = 231 cubic inches)

1 answer:

Lady_Fox [76]3 years ago

8 0

1 foot = 12 inches

(1 foot)^3 = (12 inches)^3

1 cubic foot = (12^3) cubic inches

1 cubic foot = 1728 cubic inches, will be used as a conversion factor

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Find the volume of the pool. Assume it is a rectangular prism.

Volume = length*width*height

Volume = 32*16*8

Volume = 4096 cubic feet

Multiply by 1728, which was the conversion factor found earlier, to convert from cubic feet to cubic inches.

4096 cubic feet = (4096*1728) cubic inches = 7077888 cubic inches

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Now use the fact that 1 gallon = 231 cubic inches to convert from cubic inches to gallons

7077888 cubic inches = (7077888 cubic inches)*(1 gallon/231 cubic inches) = 7077888/231 = 30640.2078 gallons which is approximate

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If x is the amount of time in minutes, then 8x gallons of water have been added after x minutes. Set this equal to 30640.2078 and solve for x

8x = 30640.2078

x = 30640.2078/8

x = 3830.02598

Divide this by 60 to convert to hours

3830.02598/60 = 63.8337663

<h3>It takes approximately 63.8 hours to fill the pool</h3>

This is approximately 63.8/24 = 2.625 days

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Step-by-step explanation:

The question is not properly presented. See attachment for proper presentation of question

From the attachment, we have that:

$W = \frac{3}{25}$

$X = \frac{\sqrt{3}}{11}$

$Y = \frac{9}{100}$

$Z = \frac{\pi}{24}$

Required

Order from greatest to least

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$W = \frac{3}{25}$

$W = 0.12$

$X = \frac{\sqrt{3}}{11}$

Take square root of 3

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$X = 0.16$ --- approximated

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$Y = 0.09$

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Take π as 3.14

$Z = \frac{3.14}{24}$

$Z = 0.13083333333$

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List out the results, we have:

$W = 0.12$ $X = 0.16$ $Y = 0.09$ $Z = 0.13$

Order from greatest to least, we have:

$X = 0.16$ $Z = 0.13$ $W = 0.12$ $Y = 0.09$

Hence, the order of arrangement is:

$X = \frac{\sqrt{3}}{11}$ $Z = \frac{\pi}{24}$ $W = \frac{3}{25}$ $Y = \frac{9}{100}$

i.e.

$\frac{\sqrt{3}}{11}, \frac{\pi}{24}, \frac{3}{25}, \frac{9}{100}$

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