Question

a rectangular prism is 4 units x 2-1/2 units by 1-1/2 units. how many cubes with a side length of 1/2 unit will completely fill the prism

Answer 1

find 2 things
1. volume of 1 cube
2. volme of rectangular prism


1. volume of a cube=side^3
side=1/2
v=1/2^3=1/8 cubic units

2. volume=legnth times widht itmes height
4
2 and 1/2
1 and 1/2

for ease, convert to improper
2 and 1/2=2+1/2=4/2+1/2=5/2
1 and 1/2=1+1/2=2/2+1/2=3/2

so
v=4/1 times 5/2 times 3/2=60/4=15

so

how many cubes does it take to fill the prism
how many cubes times volume of 1 cube=volume of prism
xcubes times 1/8unit^3=15unt^3
multiply both sides by 8/1 unit^3 to clear fraction (since 1/8 times 8/1=8/8=1)
xcubes=240

need 240 cubes to fill prism