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

Mathematics

1 answer:

SCORPION-xisa [38]4 years ago

4 0

Answer:

$\large\boxed{224\ cubes}$

Step-by-step explanation:

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

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

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