Tyler’s family is using a shipping trailer that is 5 feet tall, 4 feet wide, and 12 feet long to load boxes of apples in. Each box the apples are packed in has to have a volume of 5184 in3. Help design a box that will fill the trailer with no wasted space, and meet the volume requirements.
Analyze the information in the problem. Clearly explain your strategy for designing the box to fit the requirements.
+37170 Volume of box = 5184 in^3
Total volume of trailer is 5x4x12 x (1728) cubic inches = 414720 in^3
Number of boxes to fill will be 414720/5184= 80 boxes to fill with no wasted space
L x W x H = 5184 L must divide into 12 evenly W into 4 evenly and H into 5 evenly
12/L x 4/W x 5/H = 80
how big are the boxes that you decided to make though guest that answred this question lxwxh
+37170 Volume of box = 5184 in^3
Total volume of trailer is 5(12)x4(12)x12(12) = 414720 in^3
Number of boxes to fill will be 414720/5184= 80 boxes to fill with no wasted space
L x W x H = 5184 L must divide into 12 (144 inches) evenly W into 4 (48 inches)evenly and H into 5(60 inches) evenly
We can just ASSIGN one of these variables to find the other two....let's make W= 24 inches
then L x W x H= 5184
L x H = 5184/24=216
L x H = 216 Let's make H= 12 inches then L=18
L x W X H = 18 x 24 x 12 = 5184 CHECK ! AND L= 18 goes into 144 evenly at 8 times
H= 12 goes into 60 evenly at 5 times
W=24 goes into 48 evenly at 2 times 8x5x2= 80 boxes CHECK !
THIS is only ONE possible solution out of MANY !!!!!
+37170 "Would 1.5ft L 1ft W 1ft H wor for each box? "
Sorry, that will not work....the question states each box must be 5184 cubic inches. 1.5(12) x 12 x12 is only 2592 inches ...only 1/2 the requested volume (HINT: if you DOUBLE any ONE of the dimensions AND they still fit evenly in the alloted space, you will have an answer that will work !)
