Question

The volume of a large tank is 350 ft. It is 6ft wide and 4 2 ft high. What is the length of the tank? 3 3 Length =

Answer 1

The rule of the volume of the rectangular prism is

`V=L* W* H`

L is the length

W is the width

H is the height

Since the tank is 6 2/3 ft wide and 4 2/3 height, then

`\begin{gathered} W=6(2)/(3)=(6*3+2)/(3) \\ W=(20)/(3) \end{gathered}`
`\begin{gathered} H=4(2)/(3)=(4*3+2)/(3) \\ H=(14)/(3) \end{gathered}`

Since the volume of the tank is 350 cubic feet, then

`V=350`

Substitute them in the rule above

`\begin{gathered} 350=L*(20)/(3)*(14)/(3) \\ 350=(280)/(9)L \end{gathered}`

Divide both sides by 280/9 to find L

`\begin{gathered} (350)/((280)/(9))=L \\ (45)/(4)=L \end{gathered}`

Make it a mixed number

Since 45/4 = 11 1/4

`L=11(1)/(4)`

The length is 11 1/4 feet