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junior2461

04.08.2021

Mathematics

165 boxes

Step-by-step explanation:

Given

The dimension of the bigger box is $1\ \frac{1}{4}\times 2\ \frac{3}{4}\times \frac{3}{4}\ ft^3$

the dimension of the smaller box is $\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\ ft^3$

The volume of the large box

$\Rightarrow V_1=\dfrac{5}{4}\times \dfrac{11}{4}\times \dfrac{3}{4}=\dfrac{165}{64}\ ft^3$

The volume of the small box

$\Rightarrow V_o=\dfrac{1}{4}\times\dfrac{1}{4}\times \dfrac{1}{4}=\dfrac{1}{64}\ ft^3$

Suppose there are n small boxes

$\Rightarrow n=\dfrac{V_1}{V_o}$

$\Rightarrow n=\dfrac{\frac{165}{64}}{\frac{1}{64}}=165\ \text{boxes}$

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