Answer:
Volume of the prism :---
[tex]1cm \times \frac{7}{4}cm \times 2cm = \frac{7}{2} c {m}^{3} \\ [/tex]
Volume of the cube :---
[tex] \frac{1}{4} cm \times \frac{1}{4} cm \times \frac{1}{4} cm = \frac{1}{64} c {m}^{3} \\ [/tex]
Number of cubes :---
(Volume of the prism÷Volume of the cube)
[tex] \frac{7}{2} \div \frac{1}{64} = \frac{7}{2} \times 64 = 7 \times 32=\boxed{224 }\\ [/tex]
It takes 224 cubes with side lengths of 1/4 cm to fill the prism.
