Question

A semi trailer is being packed with boxes that are 1 1/2 feet on each edge. The cargo space of the trailer is 28 feet long, 8 1/2 feet wide, and 9 1/6 feet high. What is the maximum number of boxes that will fit inside the trailer?
Answers:

2,016

540

2,138

633

Answer 1

Answer: Last option is correct.

Step-by-step explanation:

Since we have given that

Length of the cargo space of the trailer = 28 ft

Width of the cargo space of the trailer is given by

$8\frac{1}{2}\\\\=\frac{17}{2}\ ft$

Height of the cargo space of the trailer is given by

$9\frac{1}{6}\\\\=\frac{55}{6}\ ft$

Volume of the cargo space of the trailer is given by

$Volume=length\times width\times height\\\\Volume=28\times \frac{17}{2}\times \frac{55}{6}\\\\Volume=2181.67\ cm^3$

Now. Length of each edge of a semi-trailer is given by

$1\frac{1}{2}\\\\=\frac{3}{2}\ ft$

So, Volume of semi-trailer is given by

$Volume=a^3\\\\Volume=\frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}\\\\Volume=\frac{27}{8}\\\\Volume=3.375\ ft^3$

So, Maximum number of boxes that will fit inside the trailer is given by

$\frac{\text{Volume of cargo space}}{\text{ volume of semi trailer}}\\\\=\frac{2181.67}{3.375}\\\\=646.42$

Hence, According to options, it is nearest to 633.

Therefore, Last option is correct.