Question

PLZ HELP!!!! There is a box in your kitchen pantry that is a rectangular prism. Its volume is 64 cubic inches. How many different Surface Areas are possible? What is the maximum Surface Area? What is the minimum Surface Area?

Answer 1

We know that the volume of a rectangular prism is given by:
V = A · h
where:
A = surface area 
h = height

Therefore, you can solve for A:
A = V / h
   = 64 / h

Now, you need to ask yourself by how many numbers you can divide 64. The possible heights are 64, 32, 16, 8, 4, 2 and 1.

Hence:
A) there are 7 possible surface areas (one for each possible height).

B) the maximum Area will be that of the box with the minimum height:
A = 64 / 1 = 64

C) the minimum Area will be that of the box with the maximum height:
A = 64 / 64 = 1