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Calculus-Related Rates and Optimization

Total questions: 21

Worksheet time: 2hrs 38mins

Name
Class
Date
1.

How was your weekend? I hope it went well for you!

a)

Great

b)

Good

c)

Decent

d)

Could have been better

2.

Which movie was #1 in the theaters last weekend? (March 23 and March 24)

a)

Black Panther

b)

Pacific Rim Uprising

c)

Tomb Raider

d)

Sherlock Gnomes

3.
Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?
a)
3 ft/sec
b)
-7.2 ft/sec
c)
7.2 ft/sec
d)
12
4.
Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec.  How fast is the area of the outer circle changing when the diameter is 8 in?
a)
80pi in/sec
b)
20pi in/sec
c)
60pi in/sec
d)
4opi in/sec
5.
Brandon is starting to clean up after a birthday party. He begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm3/sec.  How fast is the diameter changing when the diameter is 8 cm?
a)
-1/(16pi) cm/sec
b)
-1/16 cm/sec
c)
-1/(4pi) cm/sec
d)
1/(4pi) cm/sec
6.
Louisa and Karis were each dropped off at the same bus stop. Louisa’s bus drops her off at 3:30 whereas Karis is dropped off ten minutes later. Louisa runs home at a constant rate of 6 mph and Karis runs home at 3 mph. Louisa lives north of the bus stop and Karis lives to the east.  How fast is the distance between them changing at 4:00?
a)
6.512 mph
b)
7.115 mph
c)
6.708 mph
d)
6.641 mph
7.
A baseball diamond is a square with a side of 90 ft. Tucker hits the ball and runs towards first base at 16 ft/sec.  How fast is the distance between second base and Tucker changing when he is 30 ft from first base?
a)
8.875 ft/sec
b)
5.060 ft/sec
c)
-5.060 ft/sec
d)
-8.875 ft/sec
8.
(3 min) The area of a circular region is increasing at a rate of 96 π square meters per second. When the area of the region is 64 π square meters, how fast, in meters per second, is the radius of the region increasing?
a)
6
b)
8
c)
16
d)
4√3
9.
(3 min) The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At the instant when the surface area S becomes 100 π square inches, what is the rate of increase, in cubic inches per second, in the volume V? SA = 4 π r2 and V = (4/3) π r3
a)
30π
b)
10π
c)
12π
d)
25π
10.
A certain medical procedure requires that a balloon be inserted into the stomach and then inflated. Model the shape of the balloon by a sphere of radius r. If r is increasing at the rate of 0.3 cm/min, how fast is the volume changing when the radius is 4 cm?
a)
15.08 cm3/min
b)
268.08 cm3/min
c)
60.32 cm3/min
d)
6.03 cm3/min
11.
The radius r of a sphere is increasing at a rate of 2 inches per minute.  Find the rate of change of the volume when r=6 inches.
a)
C=2πr
b)
A=πr²
c)
V=(4/3)πr³
d)
S=4πr²
12.
All edges of a cube are expanding at a rate of 3 centimeters per second.  How fast is the volume changing each edge is 1 centimeter.
a)
A=l*w
b)
V=3s²
c)
A=s²
d)
V=s³
13.
A conical tank is 10 feet across the top and 12 feet deep.  If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water if 8 feet deep.
a)
V=(1/3)πr²h
b)
V=(4/3)πr³
c)
d=√(x²+y²)
d)
S=2lh+2lw+2hw
14.
A construction worker pulls a five meter plank up the side of a building under construction by means of a rope tied to one end of the plank.  Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of .15 meters per second.  How fast is the end of the plank sliding along the ground when when it is 2.5 meters from the wall of the building?
a)
a²+b²=c²
b)
d=√(x²+y²)
c)
h=r⋅sinθ
d)
1=sin²θ+cos²θ
15.
What was the name of the trading post in FROZEN?
a)
Anna Supplies
b)
Arrandale Goods
c)
Wandering Oakens
d)
Hans Post
16.
What type of flower was going to die if the Beast did not find love?
a)
tulip
b)
carnation
c)
rose
d)
daffodil
17.
Brie is what type of food?
a)
vegetable
b)
bread
c)
cheese
d)
fruit
18.
Name?
a)
Megatron
b)
Bumblebee
c)
Ratchet
d)
Optimus Prime
19.
Who are the Teenage Mutant Ninja Turtles?
a)
Donatello, Michelangelo,Leonardo, Raphael
b)
Donatello, Michelangelo,Leonardo,Galileo
c)
Donatello, Michelangelo, Leonardo, Vincent
d)
Donatello, Michelangelo,Leonardo, Pablo
20.
Which comic book character was not in 'THE AVENGERS'
a)
Iron Man
b)
Captain American
c)
Spiderman
d)
The Hulk
21.
What planet is the closets to earth?
a)
Venus 
b)
Mars 
c)
Saturn 
d)
Earth