On your paper, draw a diagram of a square-based pyramid if the side length of the base is $9$ cm and the height of the pyramid is $12$ cm.  

1. Find the volume of the pyramid.

   Hint (a):

   The formula to find the volume of a pyramid is $\frac{1}{3}(\text{base})(\text{height})$

   Hint 1(a):

   Calculate area of base:

   $(9)(9) = 81\text{ cm}^2$

   Hint 2(a):

   Use formula to calculate volume (a):

   $\frac{1}{3}(12)(81) = \frac{1}{3}(972) = 324\: \text{units}^3$

   

2. If a smaller pyramid is similar to the pyramid in part (a), but has a linear scale factor of $\frac { 1 } { 3 }$, find its volume.

   Hint (b):

   Find the volume of the smaller pyramid in one of two ways:
   Calculating from the dimensions or
   Using the ratio of volumes.

   More Help (b):

   Since the linear scale factor is $\frac{1}{3}$ ,the ratio of the volume is $(\frac{1}{3})^3$, $\frac{1}{27}$. 

   Answer (b):

   $(324)\left(\frac{1}{27}\right) = 12 \text{ cm}^3$