Question

A glass case is in the shape of a rectangular prism. The volume of the case is 4/125 cubic foot. How many cubic blocks with a side length of `1/5 foot would be required to find the volume of the glass case? OA. 2 B. 3 O c. 4 OD. 5

Answer 1

Step 1: Write out the formula for the volume of a cube

`V_c=s^3`
`\begin{gathered} \text{ Where} \\ V_c=\text{ the volume of the cube} \\ s-\text{ the length of one side of the cube} \end{gathered}`

Step 2: Write out the given value of the side of the square and substitute it into the formula

`s=(1)/(5)ft`
`V_c=((1)/(5))^3=(1)/(125)ft^3`

Step 3: Write out the formula to find the number of cubes of a given volume that can fill the container of a given value

`\text{ the number of cubes = }\frac{\text{ the volume of the container}}{\text{ the volume of the cube}}`

Step 4: Write out the volume of the glass case and the cube and substitute them into the formula in step 3

`\begin{gathered} \text{ the volume of the container = }(4)/(125)ft^3 \\ \text{ the volume of the cube = }(1)/(125)ft^3 \end{gathered}`

Therefore,

`\text{ the number of cubes = }((4)/(125))/((1)/(125))=(4)/(125)*(125)/(1)=4`

Hence, the number of cubes is 4

The right option is C