Question

a shipping box in the shape of a cube has edge lengths of 6 inches. it can hold 24 staplers. if the dimensions of a shipping box are all doubled, how many staplers can the larger box hold? 24 staplers 48 staplers 96 staplers 192 staplers

Explanation:

Step1: Recall volume of cube formula

The volume \( V \) of a cube with edge length \( s \) is given by \( V = s^3 \). For the original cube, \( s = 6 \) inches, so its volume is \( V_1=6^3 = 216 \) cubic inches.

Step2: Find volume of larger cube

When the dimensions are doubled, the new edge length \( s_2 = 2\times6 = 12 \) inches. The volume of the larger cube is \( V_2 = 12^3=1728 \) cubic inches.

Step3: Determine ratio of volumes

The ratio of the volume of the larger cube to the original cube is \( \frac{V_2}{V_1}=\frac{1728}{216} = 8 \). This is because if each dimension is scaled by a factor of \( k \), the volume scales by \( k^3 \), here \( k = 2 \), so \( 2^3=8 \).

Step4: Find number of staplers in larger box

Since the number of staplers a box can hold is proportional to its volume, the number of staplers in the larger box is \( 24\times8 = 192 \).

Answer:

192 staplers