# Math 212 Homework 4

```Math 212
Name: __________________________________
Homework 4
z
1. The figure to the right shows a polyhedron with five vertices,
eight edges, and five faces.
H0,1,1L
H1,0,1L
(a) Find the equation for the plane containing the points
a&quot;&szlig; !&szlig; &quot;b, a!&szlig; &quot;&szlig; &quot;b, and a&quot;&szlig; &quot;&szlig; !b.
H0,1,0L
H1,0,0L
y
x
H1,1,0L
(b) Sketch the base of this polyhedron on the following axes. Label each of the three vertices, and
indicate the equations for each of the three lines.
PRACTICE SPACE
y
y
x
x
(c) Use a double integral to find the volume of this polyhedron. You must show your work to
2. Let V be the region defined by the inequalities B#  C#  #&amp; and aB  \$b#  C# Ÿ &quot;'.
(a) Find the two points at which the circles B#  C# œ #&amp; and aB  \$b#  C# œ &quot;' intersect.
(b) Use the following axes to graph the two circles, and shade the region V .
PRACTICE SPACE
6
6
4
4
2
2
y 0
y 0
-2
-2
-4
-4
-6
-6
-4
-2
0
2
x
4
6
8
-6
-6
-4
-2
0
2
x
4
6
8
+
1+#
(c) Give a brief geometric explanation for the formula ( &Egrave;+#  B# .B œ