Question

A toy company is packaging its toys to be shipped. Each small toy is placed inside a cube-shaped box with side lengths of 1/2 These smaller boxes are then placed into a larger box with dimensions of 1/2 inch times 4 1/2 times 3 1/2.

Question 1:
What is the greatest number of small toy boxes that can be packed into each large box for shipping?

Question 2:
Use the number of small toy boxes that can be shipped in the larger box to help determine the volume of the shipping box.

Answer 1

only like 6-10 toys can be packaged into each box.

Answer 2

We can think of the dimensions of the larger box in relation to the smaller box. Since the smaller box is 1/2 inch on every side, this is not too complicated.
The larger box has sides with lengths 1/2, 4 1/2, and 3 1/2.
Along the 1/2 long side, 1 smaller box can fit. (1/2) / (1/2) = 1
Along the 4 1/2 long side, 9 smaller boxes can fit (4 1/2) / (1/2) = 9
Along the 3 1/2 long side, 7 smaller boxes can fit (3 1/2) / (1/2) = 7

Answer 3

Ok, thank you. Was this the answer for problem one or two BankrolHayden?

Answer 4

So, from that, we can figure that each larger box can fit 1 * 9 * 7 smaller boxes. That's 63 smaller boxes per larger box.
As for the second part of the question, you could multiply 63 by the volume of each of the smaller boxes.
For reference, each smaller box has a volume of 1/2*1/2*1/2 or 1/8. 63 * 1/8 = ?
You'd also get the same result by simply using the dimensions of the larger box, 1/2 * 4 1/2 * 3 1/2, so that's a way you can check that answer

Answer 5

Ok, Thank you so much :)