Answer:
<u>1. 192 books.</u>
<u>2. 96 books.</u>
<u>3. 24 books.</u>
Step-by-step explanation:
1. Let's find the volume of each book and the volume of the box, this way:
Volume of a book = 4 * 6 * 1 = 24 inches ³
Volume of the box = 24 * 24 * 8 = 4,608 inches ³
2. If Hardy fills the box completely, what is the greatest number of books that fit into the box?
Greatest number of books = Volume of the box/Volume of a book
Greatest number of books = 4,608/24
<u>Greatest number of books = 192</u>
3. If Hardy fills the box completely with the least number of layers, there will be (blank) books on the bottom layer.
The height of the box is 8 inches, so it can only can hold 2 or 8 layers of books, since the books are 4 * 6 * 1 inches.
Greatest number of layers = Height of the box/Width of a book
Greatest number of layers = 8/1 = 8
Minimum number of layers = Height of the box/Height of a book
Minimum number of layers = 8/4 = 2
Upon saying that, we have:
Number of books per layer = Greatest number of books/Minimum number of layers
<u>Number of books per layer = 192/2 = 96 </u>
4. To fill the box completely, Hardy places 8 layers of books in the box. There are (blank) books in each layer.
Number of books per layer = Greatest number of books/Number of layers
Number of books per layer = 192/8
<u> Number of books per layer = 24</u>
