Question

Can you help me with this assignment? Thx The length is 2 2/3 ft and the width is 1 1/8. The height is 1 1/3 ft.

Answer 1

Given the dimensions of the carton:

`\begin{gathered} l=2(2)/(3)ft \\ \\ w=1(1)/(8)ft \\ \\ h=1(1)/(3)ft \end{gathered}`

You can convert them to Improper Fractions as follows:

- Multiply the whole number part by the denominator.

- Add the result to the numerator.

- The denominator does not change.

Then:

`2(2)/(3)=((2\cdot3)+2)/(3)=(6+2)/(3)=(8)/(3)\Rightarrow l=(8)/(3)ft`
`1(1)/(8)=((1\cdot8)+1)/(8)=(9)/(8)\Rightarrow w=(9)/(8)ft`
`1(1)/(3)=((1\cdot3)+1)/(3)=(4)/(3)\Rightarrow h=(4)/(3)ft`

Now you need to use the following formula for calculating the volume of a rectangular prism:

`V=l\cdot w\cdot h`

Where "l" is the length, "w" is the width and "h" is the height.

Then, substituting values into the formula and evaluating, you get:

`V=((8)/(3)ft)((9)/(8)ft)((4)/(3)ft)`
`\begin{gathered} V=((8\cdot9\cdot4)/(3\cdot8\cdot3))ft^3 \\ \\ V=(288ft^3)/(72) \end{gathered}`
`V=4ft^3`

Hence, the answer is:

`V=4ft^3`