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Question Find the value of contents in a 6ft×12ft×2.5ft6 \mathrm{ft} \times 12 \mathrm{ft} \times 2.5 \mathrm{ft} container, if contents weigh 0.77 lbs/ft3^3 and are worth $4.55\$ 4.55/lb.

Studdy Solution

STEP 1

Assumptions1. The container is a right rectangular prism with dimensions 6ft6 \mathrm{ft} by 12ft12 \mathrm{ft} by .5ft.5 \mathrm{ft}. . The container is entirely full.
3. The contents of the container weigh on average0.77 pounds per cubic foot.
4. The contents of the container are worth on average $4.55\$4.55 per pound.

STEP 2

First, we need to find the volume of the container. The volume of a right rectangular prism is given by the product of its length, width, and height.
Volume=LengthtimesWidthtimesHeightVolume = Length \\times Width \\times Height

STEP 3

Now, plug in the given values for the length, width, and height to calculate the volume.
Volume=6fttimes12fttimes2.5ftVolume =6 \mathrm{ft} \\times12 \mathrm{ft} \\times2.5 \mathrm{ft}

STEP 4

Calculate the volume of the container.
Volume=6fttimes12fttimes2.ft=180ft3Volume =6 \mathrm{ft} \\times12 \mathrm{ft} \\times2. \mathrm{ft} =180 \mathrm{ft}^3

STEP 5

Now that we have the volume of the container, we can find the total weight of the contents. This can be done by multiplying the volume by the average weight per cubic foot.
Total weight=VolumetimesAverage weight per cubic footTotal\, weight = Volume \\times Average\, weight\, per\, cubic\, foot

STEP 6

Plug in the values for the volume and the average weight per cubic foot to calculate the total weight.
Total weight=180ft3times0.77lb/ft3Total\, weight =180 \mathrm{ft}^3 \\times0.77 \mathrm{lb/ft}^3

STEP 7

Calculate the total weight of the contents.
Total weight=180ft3times0.77lb/ft3=138.6lbTotal\, weight =180 \mathrm{ft}^3 \\times0.77 \mathrm{lb/ft}^3 =138.6 \mathrm{lb}

STEP 8

Now that we have the total weight of the contents, we can find the total value of the contents. This can be done by multiplying the total weight by the average value per pound.
Total value=Total weighttimesAverage value per poundTotal\, value = Total\, weight \\times Average\, value\, per\, pound

STEP 9

Plug in the values for the total weight and the average value per pound to calculate the total value.
Total value=138.6lbtimes$4.55/lbTotal\, value =138.6 \mathrm{lb} \\times \$4.55/\mathrm{lb}

STEP 10

Calculate the total value of the contents.
Total value=138.6lbtimes$4.55/lb=$630.63Total\, value =138.6 \mathrm{lb} \\times \$4.55/\mathrm{lb} = \$630.63The value of the container's contents is approximately $630.63.

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