Question

The figure below shows a rectangular prism and a cube: A rectangular prism and a cube are drawn side by side. The length of the rectangle prism is 5 inches, the width is 4 over 5 inch, and its height is 1 and 3 over 5 inches. The cube has a side length of 1 over 5 inch. How many such cubes are required to completely pack the prism without any gap or overlap? 160 800 2,548 4,000

Answer 1

`800\ cubes`

Explanation:

Step 1

Find the volume of the prism

we know that

The volume of the prism is equal to

`V=LWH`

In this problem we have

`L=5\ in`

`W=4/5\ in`

`H=1 3/5\ in=8/5\ in`

substitute the values

`V=5(4/5)(8/5)=32/5\ in^(3)`

Step 2

Find the volume of the cube

we know that

the volume of the cube is equal to

`V=b^(3)`

where

`b=1/5\ in`

substitute

`V=(1/5)^(3)=1/125\ in^(3)`

Step 3

Divide the volume of the prism by the volume of the cube

`((32/5))/((1/125))=25*32=800\ cubes`