Number 
Question 
Answer 
See the work 
1. 
What are the rectangular coordinates of the point whose cylindrical coordinates
are ?
x=
y=
z=

x= 1.236
y= 3.804
z= 1

The work 
2. 
What are the rectangular coordinates of the point whose
cylindrical coordinates
are (r = 5, &theta = 1.4, z = 6 ) ?
x =
y =
z =

x= 0.8498
y= 4.927
z= 6

The work 
3. 
What are the cylindrical coordinates of the point whose rectangular coordinates
are (x = 5, y = 1 , z = 2 ) ?
r =
&theta =
z =

r = 5.099
&theta = 0.1974
z = 2

The work 
4. 
What are the cylindrical coordinates of the point whose rectangular coordinates
are (x = 3 , y = 2 , z = 1 ) ?
r =
&theta =
z =

r = 3.6056
&theta = 2.554
z = 1

The work 
5. 
Express the point given in Cartesian coordinates in cylindrical coordinates
(r, &theta, z).
A) = (,, )
B) = (,, )
C) = (,, )
D) = (,, )

A) ( 7, 0.5236, 7)
B) ( 7, 2.61799, 7)
C) ( 7, 5.75959, 7)
D) ( 7, 3.66519, 7)

The work 
6. 
Use cylindrical coordinates to evaluate the triple integral
,
where E is the solid bounded by the circular paraboloid
and the
xyplane.

857.864 
The work 
7. 
Find the volume of the solid enclosed by the paraboloids and .

12.5664 
The work 
8. 
Find the volume of the ellipsoid
.

319.89 
The work 
9. 
What are the rectangular coordinates of the point whose spherical coordinates
are (1 , 3&pi/6, 4&pi/6 ) ?
x =
y =
z =

x = 0
y = 0.866
z = 0.5

The work 
10. 
What are the spherical coordinates of the point whose rectangular coordinates
are (4, 4,4) ?
&rho =
&theta =
&phi =

&rho = 6.9282
&theta = 0.7854
&phi = 0.95532

The work 
11. 
Express the point given in Cartesian coordinates in spherical coordinates
(&rho, &theta, &phi).
A) = (,,)
B) = (,, )
C) = (,, )
D) = (,, )

A) ( 7, 0.7854, 0.5234)
B) ( 7, 2.3562, 0.5236)
C) ( 7, 5.4978, 2.618)
D) ( 7, 3.927, 2.618) 
The work 
12. 
What are the cylindrical coordinates of the point whose spherical coordinates
are ( 5, 5, &pi/6) ?
r =
&theta =
z =

r = 2.5
&theta = 5
z = 4.3301

The work 
13. 
Use spherical coordinates to evaluate the triple integral , where E is the ball:
.

148406.324 
The work 
14. 
Use spherical coordinates to evaluate the triple integral
,
where E is the region bounded by the spheres
and
.

0 
The work 
15. 
FInd the volume of the solid that lies within the sphere
, above the xy plane, and outside the cone
.

55.779 
The work 
16. 
question 
Answer 
The work 
17. 
question 
Answer 
The work 
