PRINTABLE VERSION
Quiz 10
You scored 75 out of 100
Question 1
Your answer is INCORRECT.
Find the rate of change of the area of a square with respect to the length ​z​ , the diagonal of the
square. What is the rate when ​z=9​?
a) ​dAdz=2z; rate =18
b) ​dAdz=z; rate =18
c) ​dAdz=z; rate =9
d) ​dAdz=2z; rate =9
e) ​dAdz=z2–√; rate =92–√
Question 2
Your answer is CORRECT.
Find the rate of change of the surface area of a sphere with respect to the radius ​r​. What is the
rate when ​r=3​?
a) ​dSdr=8r​2​π; rate =72π
b) ​dSdr=4rπ; rate =12π
c) ​dSdr=2rπ; rate =6π
d) ​dSdr=8rπ; rate =24π
e) ​dSdr=4r​2​π; rate =36π
Question 3
Your answer is INCORRECT.
An object moves along a coordinate line, its position at each time ​t≥0​ is given by
x(t)=(t​2​−t)(t​2​+t)​. Find the velocity at time ​t​0​=3.
a) ​102
b) ​72
c) ​852
d) ​−102
e) ​2
Question 4
Your answer is CORRECT.
An object moves along the ​x​-axis, its position at each time ​t≥0​ is given by ​x(t)=12t​4​−83t​3​+3t​2​.
Determine the time interval(s), if any, during which the object moves right.
a) ​(0,1)∪(3,∞)
b) ​(1,3)
c) ​(0,23)∪(2,∞)
d) ​(0,12)∪(32,∞)
e) ​(0,1)∪(92,∞)
Question 5
Your answer is CORRECT.
An object projected vertically upward from ground level returns to earth in 14 seconds. Find the
initial velocity in feet per second.
a) ​220
b) ​240
c) ​224
d) ​230
e) ​234
Question 6
Your answer is CORRECT.
A stone is thrown upward from ground level. The initial speed is 128 feet per second. In how
many seconds will the stone hit the ground?
a) ​8
b) ​12
c) ​10
d) ​14
e) ​7
Question 7
Your answer is CORRECT.
A particle is moving along the parabola ​x​2​=4(y+3)​. As the particle passes through the point
(4,1)​, the rate of change of its ​y​-coordinate is 6 units per second. How fast, in units per second,
is the ​x-​ coordinate changing at this instant?
a) ​4
b) ​13
c) ​32
d) ​6
e) ​3
Question 8
Your answer is CORRECT.
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) ​59
c) ​−275
d) ​−527
e) ​5
Question 9
Your answer is CORRECT.
A rectangle is inscribed in a circle of radius 5 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 6 inches?
a) ​485​ ​in​2​/sec
b) ​48​ ​in​2​/sec
c) ​−7​ ​in​2​/sec
d) ​7​ ​in​2​/sec
e) ​−96​ ​in​2​/sec
Question 10
Your answer is CORRECT.
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 cm​3​ 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
Your answer is INCORRECT.
A 5-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 3 feet from the wall?
a) ​72
b) ​78
c) ​−74
d) ​74
e) ​−72
Question 12
Your answer is CORRECT.
A man standing 5 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 300 feet per minute, at what rate, in
feet per minute, will the length of his shadow be changing?
a) ​1080
b) ​540
c) ​−540