Suppose you were to bend two whole sheets of $8 1/2-\text{by}-11$ paper to form two cylinders (a tall, skinny one and a short, wide one). The volume of a cylinder can be calculated using the formula $V = \left(base area\right)\left(height\right)$ or $V = πr^{2}h$.

1. Do the two cylinders have the same volume? Justify your answer.

   Hint (a):

   Calculate the volume of both cylinders and compare.

   More Help (a):

   Remember, for cylinders:
   V = πr²h
   C = 2πr
   Where V is volume, r is radius, h is height, and C is circumference.

   Steps (a):

   For the tall cylinder:

   $V=\pi\left(\frac{8\frac{1}{2}}{2\pi}\right)^{2}(11)$

   $V=\pi\left(\frac{289}{16\pi^{2}}\right)(11)$

   $V=\frac{3179}{16\pi}$

   Answer (a):

   $V ≈ 63.24 \text{ in.}^{3}$

2. Is the result different if you start with $8 \frac { 1 } { 2 }$-by-$8 \frac { 1 } { 2 }$ paper?

   Hint (b):

   See part (a).