Solved on Sep 29, 2023

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

STEP 1

Assumptions1. The container is a right rectangular prism with dimensions $6 \mathrm{ft}$ by $12 \mathrm{ft}$ by $.5 \mathrm{ft}$ . . 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 $\$4.55$ 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.
$Volume = Length \\times Width \\times Height$

STEP 3

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

STEP 4

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

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.
$Total\, weight = Volume \\times Average\, weight\, per\, cubic\, foot$

STEP 6

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

STEP 7

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

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.
$Total\, value = Total\, weight \\times Average\, value\, per\, pound$

STEP 9

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

STEP 10

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

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

STEP 1

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.
$Volume = Length \\times Width \\times Height$

STEP 3

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

STEP 4

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

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.
$Total\, weight = Volume \\times Average\, weight\, per\, cubic\, foot$

STEP 6

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

STEP 7

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

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.
$Total\, value = Total\, weight \\times Average\, value\, per\, pound$

STEP 9

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

STEP 10

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

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Find the value of contents in a 6ft×12ft×2.5ft6 \mathrm{ft} \times 12 \mathrm{ft} \times 2.5 \mathrm{ft}6ft×12ft×2.5ft container, if contents weigh 0.77 lbs/ft3^33 and are worth $4.55\$ 4.55$4.55/lb.

STEP 1

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 HeightVolume=LengthtimesWidthtimesHeight

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}Volume=6fttimes12fttimes2.5ft

STEP 4

Calculate the volume of the container.Volume=6fttimes12fttimes2.ft=180ft3Volume =6 \mathrm{ft} \\times12 \mathrm{ft} \\times2. \mathrm{ft} =180 \mathrm{ft}^3Volume=6fttimes12fttimes2.ft=180ft3

STEP 5

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}^3Totalweight=180ft3times0.77lb/ft3

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}Totalweight=180ft3times0.77lb/ft3=138.6lb

STEP 8

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}Totalvalue=138.6lbtimes$4.55/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} = \$630.63Totalvalue=138.6lbtimes$4.55/lb=$630.63The value of the container's contents is approximately $630.63.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

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

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.
$Volume = Length \\times Width \\times Height$

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

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

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

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

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

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