Name: _____________________________________
Quiz Section: _______
Math 120, Quiz #5 SOLUTIONS
(Chapters 15&16, 10 pts)
1. At Papa John’s, a Large pizza has diameter of 14”, and an
Extra Large has diameter of 16”.
Suppose each pizza is cut into wedge-shaped slices, with
the vertex of the angle at the center of the pizza pie.
a) (2 pts) Which pizza slice would be larger: a slice of a
Large pizza cut at a 45º angle, or a slice of an Extra Large pizza cut at an angle of
radians?
Show work - no credit for unjustified answers.
(
)
(
)
The XL slice is a little larger.
b) (3 pts) You order a Large pizza, uncut. You love crust and want to cut the pizza yourself, to
make sure you get at least 3 square inches of crust per slice. If the toppings part of the pizza
has a 6” radius, at what minimum angle ϴ should you cut each slice? Give your answer in
degrees.
6”
7”
ϴ
2. (5 pts)
You are designing a system of wheels and belts as pictured. Wheels B and C are rigidly fastened
to the same axle, while wheels A and B are connected by a belt. You want wheel A to rotate at 2
rad/sec, and wheel C to have a linear velocity of 120 in/sec. Wheel A has radius
in, and
wheel C has radius
in.
What is the radius of wheel B? Show your work.
SOLUTION:
C
Wheel C:
A
Wheel A:
(
Wheel B:
)
B