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"ß !ß "b, a!ß "ß "b, and a"ß "ß !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
FINAL ANSWER
y
y
x
x
(c) Use a double integral to find the volume of this polyhedron. You must show your work to
receive full credit.
2. Let V be the region defined by the inequalities B#  C# € #& and aB  $b#  C# Ÿ "'.
(a) Find the two points at which the circles B#  C# œ #& and aB  $b#  C# œ "' intersect.
(b) Use the following axes to graph the two circles, and shade the region V .
PRACTICE SPACE
FINAL ANSWER
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 ( È+#  B# .B œ
. Your explanation
#
+
should include a picture as well as one or two sentences of text.
(d) Evaluate (( B .E. You must show your work to receive full credit.
V