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?
You need 3 integer factors of 12; one for each dimension. So, you could have
1x1x12
1x2x6
1x3x4
2x2x3
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?
of course, any of the four shapes I gave could be rotated to make any face the base.
To determine the number of rectangular prisms that Ginger can make by stacking all of the bead containers, we need to find the factors of 12. Factors are numbers that can be multiplied together to get a given number.
In this case, the factors of 12 are: 1, 2, 3, 4, 6, and 12. These numbers represent the possible dimensions for the base of each rectangular prism. The corresponding height of each prism would be the number of containers, which is 12.
So, Ginger can make rectangular prisms with the following bases:
- 1 inch by 12 inches
- 2 inches by 6 inches
- 3 inches by 4 inches
- 4 inches by 3 inches
- 6 inches by 2 inches
- 12 inches by 1 inch
In total, Ginger can make 6 different rectangular prisms by stacking all of the bead containers.