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=\frac{1}{5}ft$$V_c=(\frac{1}{5})^3=\frac{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

$\begin{gathered} \text{ the volume of the container = }\frac{4}{125}ft^3 \\ \text{ the volume of the cube = }\frac{1}{125}ft^3 \end{gathered}$

Therefore,

$\text{ the number of cubes = }\frac{\frac{4}{125}}{\frac{1}{125}}=\frac{4}{125}\times\frac{125}{1}=4$

Hence, the number of cubes is 4

The right option is C