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

Explanation:

Given

The dimension of the bigger box is
`1\ (1)/(4)* 2\ (3)/(4)* (3)/(4)\ ft^3`

the dimension of the smaller box is
`(1)/(4)* (1)/(4)* (1)/(4)\ ft^3`

The volume of the large box

`\Rightarrow V_1=(5)/(4)* (11)/(4)* (3)/(4)=(165)/(64)\ ft^3`

The volume of the small box

`\Rightarrow V_o=(1)/(4)*(1)/(4)* (1)/(4)=(1)/(64)\ ft^3`

Suppose there are n small boxes

`\Rightarrow n=(V_1)/(V_o)`

`\Rightarrow n=((165)/(64))/((1)/(64))=165\ \text{boxes}`