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QuestionFind the mass of water in a pool measuring 75ft×50.0ft×7.310ft75 \mathrm{ft} \times 50.0 \mathrm{ft} \times 7.310 \mathrm{ft} with sig figs.

Studdy Solution

STEP 1

Assumptions1. The length of the pool is75 ft. The width of the pool is50.0 ft3. The depth of the pool is7.310 ft4.1 ft =12 inches5.1 inch =.54 cm6. The density of water is0.998 g/mL7. The pool is completely filled with water

STEP 2

First, we need to find the volume of the pool in cubic feet. We can do this by multiplying the length, width, and depth.
Volume_{ft^} = Length_{ft} \\times Width_{ft} \\times Depth_{ft}

STEP 3

Now, plug in the given values for the length, width, and depth to calculate the volume in cubic feet.
Volumeft3=75 fttimes50.0 fttimes7.310 ftVolume_{ft^3} =75\,ft \\times50.0\,ft \\times7.310\,ft

STEP 4

Calculate the volume in cubic feet.
Volumeft3=75 fttimes50.0 fttimes7.310 ft=27382. ft3Volume_{ft^3} =75\,ft \\times50.0\,ft \\times7.310\,ft =27382.\,ft^3

STEP 5

To convert the volume from cubic feet to cubic centimeters (which is equivalent to milliliters), we need to use the conversion factors given. First, we convert from cubic feet to cubic inches, then from cubic inches to cubic centimeters.
Volumecm3=Volumeft3times(12 in/ft)3times(2.54 cm/in)3Volume_{cm^3} = Volume_{ft^3} \\times (12\,in/ft)^3 \\times (2.54\,cm/in)^3

STEP 6

Plug in the values for the volume in cubic feet and the conversion factors to calculate the volume in cubic centimeters.
Volumecm3=27382.5 ft3times(12 in/ft)3times(2.54 cm/in)3Volume_{cm^3} =27382.5\,ft^3 \\times (12\,in/ft)^3 \\times (2.54\,cm/in)^3

STEP 7

Calculate the volume in cubic centimeters.
Volumecm3=27382.5 ft3times(12 in/ft)3times(2.54 cm/in)3=775000000 cm3Volume_{cm^3} =27382.5\,ft^3 \\times (12\,in/ft)^3 \\times (2.54\,cm/in)^3 =775000000\,cm^3

STEP 8

Now that we have the volume in cubic centimeters, we can find the mass of the water in the pool by multiplying the volume by the density of water.
Massg=Volumecm3timesDensityg/cm3Mass_{g} = Volume_{cm^3} \\times Density_{g/cm^3}

STEP 9

Plug in the values for the volume in cubic centimeters and the density of water to calculate the mass.
Massg=775000000 cm3times.998 g/cm3Mass_{g} =775000000\,cm^3 \\times.998\,g/cm^3

STEP 10

Calculate the mass of the water in the pool.
Massg=775000000 cm3times0.998 g/cm3=773500000 gMass_{g} =775000000\,cm^3 \\times0.998\,g/cm^3 =773500000\,gThe mass of the water in the pool is773500000 g.

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