has climbed up 6 feet of the ladder, the ladder makes an angle of
π
/3 with the ground. Answer the two
related rates questions below. (Hint: Use two carefully labeled similar right triangles.)
(a) If
h
is the height of the firefighter above the ground, at the instant the angle of the ladder
with the ground is
π
/3, find
dh/dt=
$$
√
3
·
(1
−
622)
feet/sec.
(b) If
w
is the horizontal distance from the firefighter to the wall, at the instant the angle of the
ladder with the ground is
π
/3, find
dw/dt
$$2
−
1822
=

10.
3/3 points |
Previous Answers
(Old Final Exam Problem-Sp2009)
An hourglass is made up of two glass cones connected at their tips. Both cones have radius 1 inch and

12/14/16, 3)59 PM
hw17S3.9
Page 7 of 7
height 3 inches. When the hourglass is flipped over, sand starts falling to the lower cone.
(a) When the sand remaining in the
upper cone
has height
y
inches, its volume
A
in terms of
y
is
$$
π
27
y
3
.
(b) When the sand in the
lower cone
has reached a height of
h
inches, its volume
B
in terms of
h
is
$$
π−π
27(3
−
h
)3
. (Hint:
B
is the volume of the bottom cone minus the volume of the
empty space above the sand.)
(c) Assume the total volume of sand in the hourglass is 3
π
/4 cubic inches. Also, assume the
height of the sand in the upper cone is decreasing at a rate of
7
/100 inches per second. At the
instant when the sand in the lower cone is 1 inch high, the height of the sand in the lower cone
is increasing at a rate of
$$7100((54)(23)4)
inches per second.