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Quiz 10
Question 1
Find the rate of change of the area of a circle with respect to the radius r. What is the rate when
r=9 ?
a)
dA
= 2πr; rate = 2π
dr
b)
dA
= πr; rate = 18π
dr
c)
dA
= 2πr; rate = 18π
dr
d)
dA
= πr; rate = 9π
dr
e)
dA
= 2πr; rate = 162π
dr
Question 2
Find the rate of change of the surface area of a sphere with respect to the radius r . What is the
rate when r = 6 ?
a)
dV
= 8rπ; rate = 48π
dr
b)
dV
= 2rπ; rate = 12π
dr
c)
dV
= 4rπ; rate = 24π
dr
d)
dV
= 4r 2 π; rate = 144π
dr
e)
dV
= 8r 2 π; rate = 288π
dr
Question 3
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An object moves along a coordinate line, its position at each time t ≥ 0 is given by
x(t) = −t 2 + 2t + 1 . Find the acceleration at time t 0 = 4.
a)
0
b)
6
c)
−2
d)
10
e)
−14
Question 4
An object moves along the x -axis, its position at each time t ≥ 0 is given by
1
x(t) = − t 4 + 48t 2 . Determine the time interval(s), if any, during which the object slows
2
down.
a)
(4, 4√ 3)
b)
(6, 4)
c)
(4, 8√ 3)
d)
(4√ 3, 8√ 3)
e)
(4, 2√ 3)
Question 5
An object is dropped and hits the ground 1.5 second(s) later. From what height, in feet, was it
dropped?
a)
36
b)
46
c)
32
d)
52
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e)
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42
Question 6
A stone is thrown upward from ground level. The initial speed is 224 feet per second. In how
many seconds will the stone hit the ground?
a)
13
b)
18
c)
14
d)
20
e)
16
Question 7
A particle is moving along the parabola x 2 = 4 (y + 3) . As the particle passes through the point
(10, 22) , the rate of change of its y -coordinate is 2 units per second. How fast, in units per
second, is the x -coordinate changing at this instant?
a)
3
5
b)
10
c)
2
5
d)
15
e)
22
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 5 cubic meters per minute, find the rate of change of an edge, in
meters per minute, of the cube when the volume is exactly 27 cubic meters.
a)
−27
b)
5
9
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c)
−
27
5
d)
−
5
27
e)
5
Question 9
A rectangle is inscribed in a circle of radius 5 inches. If the length of the rectangle is decreasing at
the rate of 3 inches per second, how fast is the area changing at the instant when the length is 6
inches?
a)
72 2
in /sec
5
b)
−
c)
21 2
in /sec
2
d)
−144 in 2 /sec
e)
48 in 2 /sec
21 2
in /sec
2
Question 10
A spherical snowball is melting in such a manner that its radius is changing at a constant rate,
decreasing from 33 cm to 15 cm in 30 minutes. At what rate, in cm3 per minute, is the volume of
the snowball changing at the instant the radius is 5 cm?
a)
−50π
b)
−60π
c)
−120π
d)
30π
e)
450π
Question 11
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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)
119
2
b)
119
8
c)
119
4
d)
−
119
4
e)
−
119
2
Question 12
A man standing 7 feet from the base of a lamppost casts a shadow 6 feet long. If the man is 6 feet
tall and walks away from the lamppost at a speed of 350 feet per minute, at what rate, in feet per
minute, will the length of his shadow be changing?
a)
150
b)
600
c)
−600
d)
−300
e)
300
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