Question

A box is in the shape of a rectangular prism. Nicole is trying to ship boxes of her homemade peanut butter cookies. The box she is using to ship has the dimensions of 10in by 10in by 12in. Each cookie box has dimensions of 2in by 5in by 3in. How many cookie boxes will fit into the box to be shipped? Explain how you got your answer.

Answer 1

Answer:

Number of cookie boxes will fit into the large box  = 40

Step-by-step explanation:

Length breadth and height are given in order.

Size of large box = 10 in x 10 in x 12 in

Size of small box = 2 in x 5 in x 3 in

Complete volume of large box can be utilized since length breadth and height of large box is multiple of small box.

Volume of large box = 10 x 10 x 12 = 1200 in³

Volume of small box = 2 x 5 x 3 = 30 in³

Number of cookie boxes will fit into the large box  

                 $=\frac{\texttt{Volume of large box}}{\texttt{Volume of small box}}=\frac{1200}{30}=40$

Number of cookie boxes will fit into the large box  = 40

Answer 2

So L = x-4, W = x-4, H = x 
  
Volume = length * width * height 
 
V = L * W * H 
 
V = (x-4)*(x-4)*x 
 
V = ???

x is the height, so x-4 is the length and also the width since length and a width of 4in. less than the height