of the spherical segment is given by this formula (which we will assume):
V
= (
π
/3)
H
(27 –
H
2
).
Give EXACT ANSWERS to the questions below.
(a) Find the volume of the spherical segment if
H=1
$$26
π
3
(b) Find the rate of change of the volume with respect to
H
of the spherical segment at
H=1
:
:

(c) Use the tangent line approximation at
H=1
to estimate the value of
H
that will yield a spherical segment having volume 25
cubic inches:

10.
6/6 points |
Previous Answers
In the triangle pictured, let
A, B, C
be the angles at the three vertices, and let
a,b,c
be the sides opposite those angles.

12/14/16, 3)58 PM
hw18S3.10
According to the ``law of sines,'' you always have:
b
a
=
sin
B
sin
A
Suppose that
a
and
b
are pieces of metal which are hinged at
C
. At first the angle
A
is
π
/4 radians=45
o
and the angle
B
is
π
/3 radians
= 60
o
. You then widen
A
to 46
o
, without changing the sides
a
and
b
. Our goal in this problem is to use the tangent line approximation
to estimate the angle
B
(a) Notice that the angle
B
is a function of the angle
A
; i.e.
B=f(A)
. Consequently, it makes sense to calculate the implicit
derivative:
.

Page 10 of 11

(c) Write the linear approximation of
f
at
A
=
π
/4:

12/14/16, 3)58 PM
hw18S3.10
Page 11 of 11
(d) Using (c), when
A
= 46
o
,
B
is approximately
$$61.732
degrees; either answer exactly or to three decimal places.
11.
2/2 points |
Previous Answers
A metal rod 1 meter in length is placed horizontally on the
x
-axis, with its ends located at the points
P
= (0,0) and
Q
= (1,0). A
second long metal rod is attached to the first one at the point
Q
=(1,0) and makes an angle of 45
o
with the first. A third long metal
rod is attached to the first rod at the point
P
=(0,0) and is free to rotate about
P
. Thus, the angle
θ
made by the first and third bars is
free to change. For
θ
between 0
o
and 90
o
the second and third bars cross at a point
R
=(x,y) (see figure).