Question

How many cubes with side lengths of 1/4 does it take to fill the prism?​

Answer 1

224

Explanation:

Khan besties :)

Answer 2

`\large\boxed{224\ cubes}`

Explanation:

`\bold{METHOD\ 1}\\\\\text{Calculate the volume of a prism:}\\\\V_(p)=(2)\left((7)/(4)\right)(1)=3.5\ cm^3\\\\\text{Calculate the volume of a cube:}\\\\V_c=\left((1)/(4)\right)^3=(1)/(64)\ cm^3\\\\\text{Calculate how many times the volume of the prism is greater}\\\text{than the volume of the cube:}\\\\(V_p)/(V_c)=(3.5)/((1)/(64))=3.5\cdot64=224`

`\bold{METHOD\ 2}\\\\2cm:(1)/(4)cm=2\cdot4=8\\\\(7)/(4)cm:(1)/(4)cm=(7)/(4)\cdot(4)/(1)=7\\\\1cm:(1)/(4)cm=1\cdot4=4\\\\8\cdot7\cdot4=224\ (cubes)`