3. Riley finds out that Cooper’s Storage and Shipping Company is working with a local business to package some office supplies. Some of the supplies are packed inside a cube-shaped box with side lengths of 4.5 in. These boxes are then packed into a shipping box with dimensions of 18 in. × 9 in. × 4.5 in. How many boxes of office supplies can be packed into the larger box for shipping? Show your work.

Question

3. Riley finds out that Cooper’s Storage and Shipping Company is working with a local business to package some office supplies. Some of the supplies are packed inside a cube-shaped box with side lengths of 4.5 in. These boxes are then packed into a shipping box with dimensions of 18 in. × 9 in. × 4.5 in.  How many boxes of office supplies can be packed into the larger box for shipping? Show your work.

danjs · Answer

First need to find the volume of the small box and the large shipping box

danjs · Answer

Volume of Cube = (side length)^3

Volume of Box = length x width x height

anonymous · Answer

729

danjs · Answer

Then the number of cubes that will fit in the box is 

$$\frac{ Volume ~of~box }{ ~volume ~of ~cube }$$

danjs · Answer

what is the volume of the small box

danjs · Answer

volume of cube = (side length)^3 = side length x side length x side length

anonymous · Answer

91

danjs · Answer

divide the larger volume 729 by the smaller volume 91.125

anonymous · Answer

8.0098

danjs · Answer

729/91.125 = 8

danjs · Answer

so 8 boxes will fit in the larger box

anonymous · Answer

you're a good teacher

danjs · Answer

thanks :)