Question

mary has 50 earring boxes. the boxes measure 1 inch on each side. how many rectangular prisms, each with a different sized base, could mary make by stacking all of the earring boxes?

Answer 1

Given:
50 earring boxes
1 inch on each side

Volume = a³ = (1 in)³ = 1 in³
1 in³ x 50 boxes = 50 in³

Let us do a prime factorization:
50 ÷ 2 = 25
25 ÷ 5 = 5

1 x 2 x 5 x 5

probable dimensions of the rectangular prisms

height x width x length
1 x 1 x 50
1 x 2 x 25
1 x 5 x 10

The can make 3 rectangular prisms based on the probable dimension.