# Quiz 10 8th attempt ```PRINTABLE VERSION
Quiz 10
You scored 74 out of 100
Question 1
Find the rate of change of the volume of a sphere with respect to the radius ​r​ . What is the rate
when ​r=7​?
a) ​dVdr=4r​2​π; rate =98π
b) ​dVdr=4rπ; rate =28π
c) ​dVdr=4r​2​π; rate =196π
d) ​dVdr=2rπ; rate =14π
e) ​dVdr=2r​2​π; rate =98π
Question 2
The area of a sector in a circle is given by the formula: ​A=12r​2​θ​ , where ​r​ is the radius and ​θ​ is
the central angle measured in radians. Find the rate of change of ​θ with respect to r if A
remains constant. What is the rate when r=2?
a) ​dθdr=2Ar​2​; rate=8A
b) ​dθdr=−3Ar​3​; rate=−38A
c) ​dθdr=−4Ar​3​; rate=−12A
d) ​Not possible.
e) ​dθdr=−2Ar​3​; rate=−14A
Question 3
An object moves along a coordinate line, its position at each time ​t≥0​ is given by ​x(t)=−t​2​+t+4​.
Find the position at time ​t​0​=5.
a) ​−26
b) ​−16
c) ​−9
d) ​−86
e) ​4
Question 4
An object moves along the ​x​-axis, its position at each time ​t≥0​ is given by
x(t)=14t​4​−83t​3​+152t​2​. Determine the time interval(s), if any, during which the object moves
right.
a) ​(3,5)
b) ​(0,3)∪(5,∞)
c) ​(0,3)∪(152,∞)
d) ​(0,32)∪(52,∞)
e) ​(0,2)∪(103,∞)
Question 5
An object projected vertically upward from ground level returns to earth in 26 seconds. Find the
initial velocity in feet per second.
a) ​426
b) ​416
c) ​412
d) ​432
e) ​422
Question 6
A stone is thrown upward from ground level. With what minimum speed should the stone be
thrown so as to reach a height of 49 feet?
a) ​64​ feet/sec
b) ​54​ feet/sec
c) ​88​ feet/sec
d) ​56​ feet/sec
e) ​72​ feet/sec
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?
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 3 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.
a) ​−116
b) ​−16
c) ​−48
d) ​3
e) ​316
Question 9
A rectangle is inscribed in a circle of radius 3 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 4 inches?
a) ​−165–√​ ​in​2​/sec
b) ​−45–√5​ ​in​2​/sec
c) ​85–√3​ ​in​2​/sec
d) ​45–√5​ ​in​2​/sec
e) ​85–√​ ​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 37 cm to 17 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 8 cm?
a) ​−482π3
b) ​256π3
c) ​1280π
d) ​−1024π3
e) ​−512π3
Question 11
A 13-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 3 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 5 feet from the wall?
a) ​−1198
b) ​11916
c) ​1198
d) ​1194
e) ​−1194
Question 12