Question 118004: HELP!: 30 identical cylindrical cans of fruit juice of radius 3cm and height 12cm are arranged in 6 rows of 5 each and packed in a rectangular box.
Calculate the amount of empty space in the box. ( Use pi-3.14)
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! The strategy you should consider here is to find the total volume of the 30 cans and find the total volume of the rectangular box, then subtract the smaller from the larger to find the volume of the box not occupied by the 30 cans.
Let's do the cans first. Since the 30 cans are identical, we'll find the volume of one of the cans and multiply this by 30 to get the the total volume occupied by 30 cans.
 Substituting r = 3, h = 12, and 
 cu.cm ...This is the volume of 1 can, so we'll multiply by 30 (6 rows X 5 = 30) to get the total volume occupied by the 30 cans.
 cu.cm This is the total volume occupied by the 30 cans.
Now we'll do the box. Since you provide no dimensions for the box, we'll assume that the cans are tightly packed with no space at the top or on the sides of the box.
So, using these assumptions, we need to find the dimensions of the box.
The height of the box should be equal to the height of the cans, or, h = 12 cm.
The width, W, of the box will be equal to 5 times the diameter of each can, or 5 X 6 = 30 (Diameter = 2 X radius = 2(3cm) = 6cm)
The length, L, of the box will be equal to 6 times the diameter of each can, or 6 X 6cm = 36cm
Now we can do the volume of the box:
 Substituting L = 36cm, W = 30cm and h = 12cm.
 cu.cm
Now we'll subtract the total volume of the cans from the volume of the box to find the unoccupied space in the box.
 cu.cm. This is the volume of empty space inside the box.
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