1. Challenge Problem #1 By: Madeline Smith & Carrie Timmerman

2. Meet the very hungry Baby Pheven.

3. Baby Pheven is smaller than his food.  (We don’t want to over feed him. To keep track of how much he is eating we should find the volume of the peanut.)

4. So let’s cut his food in half to form what appears to be almost two spheres!

5. The given dimensions of the peanut are as follows: x² + 4x + y² - 2y + z² + 4z + 5 = 0 (x² + 4x + y² - 2y + z² + 4z = -5) x² + y² + z² = 4

6. x² + 4x + ___ + y² - 2y + ____ + z² + 4z + ___ = -5 ( x )² + ( y )² + ( z )² = 4 Looking at the first equation, Carrie thought we could get more out of the equation by completing the square!

7. What can we get from this? Equation 1:  ( x + 2 )² + ( y - 1 )² + ( z + 2 )² = 4  Center= (-2, 1, -2)  Radius= 2 Equation 2:  x² + y² + z² = 4  Center= (0, 0, 0)  Radius= 2

8. By graphing the two circles on a 2D plane we can find the edges of a single sphere.