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

5 in.*.8 in*1.6 in =6.4 in^3 (Volume of rectangular prism)
.2^3=0.008 in^3 (Volume of cube)
6.4/0.008=800
so basically the answer is 800 cubes

Answer 2

Answer:

$800\ cubes$

Step-by-step 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

$\frac{(32/5)}{(1/125)}=25*32=800\ cubes$