Question

17. A company ships notepads in rectangular boxes that each have inside dimensions measuring 9 inches long, 9 inches wide, and 12 inches tall. Each notepad is in the shape of a cube with an edge length of 3 inches. What is the maximum number of notepads that will fit in 1 closed box? A. 10 B. 11 C. 12 D. 22 E. 36

Answer 1

The volume of each box is:

$V=\text{length}\cdot\text{width}\cdot\text{height}$

Substituting with length = 9 in, width = 9 in, and height = 12 in, we get:

$\begin{gathered} V=9\cdot9\cdot12 \\ V=972in^3 \end{gathered}$

The volume of each notepad is:

$V=\text{length}^3$

Substituting with length = 3 in, we get:

$\begin{gathered} V=3^3 \\ V=27in^3 \end{gathered}$

The number of notepads that fit in 1 box is obtained dividing the volume of the box by the volume of each notepad, as follows:

$\frac{972in^3}{27in^3}=36\text{ notepads}$