Question

julian owns a moving company and has a truck that measures 15 ft. x 7.5 ft. x 7.5 ft. he charges customers by the number of boxes they need to put in the moving truck. if each box is a cube with a side length of 1.5 ft., how many boxes can fit in the truck?

Explanation:

Step1: Calculate truck volume

The truck is a rectangular prism, so volume \( V_{truck} = l \times w \times h \).
Given \( l = 15 \) ft, \( w = 7.5 \) ft, \( h = 7.5 \) ft.
\( V_{truck} = 15 \times 7.5 \times 7.5 \)
\( V_{truck} = 15 \times 56.25 = 843.75 \) cubic feet.

Step2: Calculate box volume

Each box is a cube, so volume \( V_{box} = s^3 \), where \( s = 1.5 \) ft.
\( V_{box} = 1.5^3 = 1.5 \times 1.5 \times 1.5 = 3.375 \) cubic feet.

Step3: Find number of boxes

Divide truck volume by box volume: \( \text{Number of boxes} = \frac{V_{truck}}{V_{box}} \)
\( \text{Number of boxes} = \frac{843.75}{3.375} = 250 \)

Answer:

250