PRINTABLE VERSION
Quiz 10
Question 1
Find the rate of change of the volume of a sphere with respect to the radius . What is the rate when
?
f
4
a)
b)
c)
DV
AT
3
ITP
451T 3r2
4IT r
2
d)
e)
Question 2
Find the rate of change of the surface area of a sphere with respect to the radius . What is the rate when
?
a)
SA
b)
DSA
DT
4th
81T r
c)
d)
e)
Question 3
An object moves along a coordinate line, its position at each time
the velocity at time
is given by
. Find
a)
b)
Htt
X
CH
V 5
5
at
lot 5
5
c)
d)
e)
Question 4
is given by
O
Determine the time interval(s), if any, during which the object moves right.
An object moves along the -axis, its position at each time
a)
Ob)
c)
d)
e)
Lt
DI
dt
a
x
.
O
t
t
6
s
Z
7 t the t
2
t
t
t
t
6
t
O l
7t t 6
A
t
O
O
6
Question 5
An object is dropped and hits the ground 4.5 second(s) later. From what height, in feet, was it dropped?
a)
b)
c)
d)
e)
Question 6
A stone is thrown upward from ground level. The initial speed is 256 feet per second. In how many seconds
will the stone hit the ground?
a)
b)
c)
d)
e)
Question 7
A particle is moving along the parabola
. As the particle passes through the point
, the
rate of change of its -coordinate is 2 units per second. How fast, in units per second, is the -coordinate
changing at this instant?
a)
b)
c)
d)
e)
Question 8
A heap of rubbish in the shape of a cube is being compacted into a smaller cube. Given that the volume
decreases at a rate of 2 cubic meters per minute, find the rate of change of an edge, in meters per minute, of
the cube when the volume is exactly 64 cubic meters.
O
b)
c)
d)
e)
x
2 mymin
d
x
a)
find date
q
V
2 3 4 2dL
dt
X
when
64
4
Question 9
A rectangle is inscribed in a circle of radius 4 inches. If the length of the rectangle is decreasing at the rate of
2 inches per second, how fast is the area changing at the instant when the length is 5 inches?
a)
b)
c)
d)
e)
Question 10
A spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing
from 28 cm to 18 cm in 30 minutes. At what rate, in cm3 per minute, is the volume of the snowball changing
at the instant the radius is 4 cm?
V
a)
du
DI
b)
du
c)
dt
d)
first
3 r2
adf.fm
DI
dt
411 1412
botcmfnin
de Tcm min
de
Ys
e)
Question 11
2 15
notes
A 39-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the
wall at the rate of 2 feet per second, at what rate is the area of the triangle formed by the wall, the ground,
and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 15 feet from the
wall?
a)
b)
c)
d)
e)
Question 12
example 7
A man standing 7 feet from the base of a lamppost casts a shadow 9 feet long. If the man is 6 feet tall and
walks away from the lamppost at a speed of 450 feet per minute, at what rate, in feet per minute, will the
length of his shadow be changing?
a)
b)
c)
d)
e)