Use the rectangular prism shown at right to complete parts (a) through (d) below.  

1. Calculate the surface area of the prism. Show all of your subproblems.

   Hint 1 (a):

   To find the surface area, find the area of each face of the prism.

   Hint 2 (a):

   There are $6$ faces in a rectangular prism.
   Each of the three different faces shown in the image have an opposite face, so find the area of each of those $3$ faces and multiply it by $2$.

   

2. Explain why the exponent for area units is $2$ (that is, cm^{$^{2}$}).

   Hint (b):

   How many terms do you multiply together to find area?

   Answer (b):

   To find area, you multiply two dimensions.
   Just as $(x)(x)=x^2,(\text{cm})(\text{cm})=\text{cm}^2$.

3. Calculate the volume of the prism.

   Hint (c):

   To find the volume of a rectangular prism, multiply the base, height, and width together.

   More Help (c):

   $\text{Volume}=(12\ \text{cm})(4\ \text{cm})(3\ \text{cm})$

   

4. Explain why the exponent for volume units is a $3$ (that is, $\text{cm}^{3}$).

   Hint (d):

   See part (b).