Question

A box with dimensions 1 1⁄4 ft x 2 3⁄4 ft x 3⁄4 ft was being filled with smaller boxes. Each of the smaller boxes are shaped like a cube. The smaller cube shaped boxes have the dimensions 1⁄4 ft x 1⁄4 ft x 1⁄4 ft. How many of the 1⁄4 ft x 1⁄4 ft x 1⁄4 ft cubes can be packed into the larger box?

Answer 1

Answer: 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

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

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