You need 3 integer factors of 12; one for each dimension. So, you could have
1x1x12
1x2x6
1x3x4
2x2x3
Ginger has 12 plastic bead containers. The containers measure 1 inch on each side. How many rectangular prisms, each with a different-sized base, could Ginger make by stacking all of the bead containers?
3 answers
total volume must be 12 inches^3
How do we get 12? V = l*w*h = base * h
1*2*6 <--the first 2 form the base, the third forms the height, base must have 2 different numbers.
but 2*3*2 would be the same as 3*2*2 , same base of 3*2
the others are:
1*3*4
1*4*3
1*6*2
2*3*2
2*6*1
3*4*1
I see a total of 7 ways
can you think of any others?
How do we get 12? V = l*w*h = base * h
1*2*6 <--the first 2 form the base, the third forms the height, base must have 2 different numbers.
but 2*3*2 would be the same as 3*2*2 , same base of 3*2
the others are:
1*3*4
1*4*3
1*6*2
2*3*2
2*6*1
3*4*1
I see a total of 7 ways
can you think of any others?
of course, any of the four shapes I gave could be rotated to make any face the base.