# Quiz 10 4th attempt

```PRINTABLE VERSION
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=6​?
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=5​?
a) ​dSdr=2rπ; rate =10π
b) ​dSdr=4r​2​π; rate =100π
c) ​dSdr=8rπ; rate =40π
d) ​dSdr=4rπ; rate =20π
e) ​dSdr=8r​2​π; rate =200π
Question 3
An object moves along a coordinate line, its position at each time ​t≥0​ is given by ​x(t)=−t​2​+t+2​.
Find the position at time ​t​0​=5.
a) ​2
b) ​−9
c) ​−18
d) ​−28
e) ​−88
Question 4
PRINTABLE VERSION
Quiz 10
An object moves along the ​x​-axis, its position at each time ​t≥0​ is given by ​x(t)=−54t​4​+120t​2​.
Determine the time interval(s), if any, during which the object ​slows down​.
a) ​(4,43–√)
b) ​(4,23–√)
c) ​(4,83–√)
d) ​(43–√,83–√)
e) ​(15,4)
Question 5
An object projected vertically upward from ground level returns to earth in 20 seconds. Find the
initial velocity in feet per second.
a) ​330
b) ​326
c) ​336
d) ​320
e) ​316
Question 6
A falling stone is at a certain instant 170 feet above the ground and 2 seconds later it is only 10
feet above the ground. From what height was it dropped?
a) ​207​ feet
b) ​208​ feet
c) ​209​ feet
d) ​206​ feet
e) ​204​ feet
Question 7
A particle is moving along the parabola ​x​2​=4(y+4)​. As the particle passes through the point
(6,5)​, the rate of change of its ​y​-coordinate is 5 units per second. How fast, in units per second,
is the ​x-​ coordinate changing at this instant?
PRINTABLE VERSION
Quiz 10
a) ​2
b) ​53
c) ​12
d) ​6
e) ​43
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 125 cubic meters.
a) ​−15
b) ​15
c) ​5
d) ​−115
e) ​−75
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 3 inches per second, how fast is the area changing at the instant when the length
is 4 inches?
a) ​83–√​ ​in​2​/sec
b) ​163–√​ ​in​2​/sec
c) ​−483–√​ ​in​2​/sec
d) ​63–√​ ​in​2​/sec
e) ​−83–√​ ​in​2​/sec
Question 10
A spherical snowball is melting in such a manner that its radius is changing at a constant rate,
decreasing from 27 cm to 18 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 2 cm?
a) ​26π5
PRINTABLE VERSION
Quiz 10
b) ​36π
c) ​−48π5
d) ​12π5
e) ​−24π5
Question 11
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) ​1192
b) ​1198
c) ​1194
d) ​−1194
e) ​−1192
Question 12
A man standing 12 feet from the base of a lamppost casts a shadow 4 feet long. If the man is 6
feet tall and walks away from the lamppost at a speed of 100 feet per minute, at what rate, in
feet per minute, will the length of his shadow be changing?
a) ​2003
b) ​−2003
c) ​−1003
d) ​503
e) ​1003
```
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