Problems and Projects
1
PROBLEMS AND PROJECTS
1. Find the highest power of 2 that can be evaluated
with a scientific or graphing calculator.
Figure
2. Find the highest power of 7 that can be evaluated
with a scientific or graphing calculator.
3. While in Switzerland, you see a Rolex watch that
a close friend wants. You send him the following
e-mail message:
Name
a
Perimeter/
circumference
b
c
b
a
c
d
E-Mail
D
ROLEX WATCH $10,800. SHOULD I BUY IT FOR YOU?
(p is approximately 3.1416)
Your friend responds as follows:
1. Find the perimeter of a rectangular garden with
dimensions of 12 meters by 18 meters.
E-Mail
NO PRICE TOO HIGH! REPEAT... NO! PRICE TOO HIGH.
Would you buy the watch? Why or why not? What
is wrong with your friend’s message? What mathematical principle does this example illustrate?
4
6
2⫹4⫹6
12
4. Note that 3 ⫽ 6 ⫽ 9 ⫽ 3 ⫹ 6 ⫹ 9 , which is 18. Is
this principle always true? That is, is
2
2. Find the circumference of a circle with a radius of
3.8 feet. Give the answer to the nearest
hundredth.
Project 2
Complete the table and work the problems that
follow.
Figure
a
c
e
a⫹c⫹e
⫽ ⫽ ⫽
b
d
ƒ
b⫹d⫹ƒ
s
Can you prove it? Is
s
a
c
e
g
a⫹c⫹e⫹g
⫽ ⫽ ⫽ ⫽
b
d
ƒ
h
b⫹d⫹ƒ⫹h
For how many fractions is this principle true?
l
w
Project 1
Complete the table and work the following problems.
Figure
Name
r
Perimeter/
circumference
h
s
s
s
Square
b
P ⫽ 4s
b2
s
h
w
l
Name
b1
Square
Area
A ⫽ s2
2
Chapter 0
A Review of Basic Algebra
Figure
Name
Area
5. Find the volume of a sphere with a radius of
20.5 feet.
6. Find the volume of a 10-foot-long cylinder whose
base is a circle with a radius of 1.6 feet.
s
7. Find the volume of a cone with a circular base
15 centimeters in diameter and a height of
12.5 centimeters.
s
s
h
l
8. Find the volume of a pyramid whose rectangular
base has dimensions of 8.7 meters by 9.3 meters
and whose height is 15.8 meters.
w
r
h
r
h
Project 3
A village council is debating whether or not to build
an emergency water reservoir for use in drought conditions. The tentative plan calls for a conical reservoir
with a diameter of 173 feet and height of 87.2 feet.
During drought conditions, the reservoir will lose
water to evaporation as well as supply the village with
water. The company that designed the reservoir provided the following information.
If D equals the number of consecutive days the
reservoir is used to provide water, the total amount E
(in cubic feet) of water lost to evaporation will be
E ⫽ 0.1V a
r
h
The water left in the reservoir after it has been used
for D days will be
*B represents the area of the base.
Give each answer to the nearest hundredth.
1. Find the area of a circle with a diameter of
21 feet.
2. Find the area of a triangle with a base of
21.3 centimeters and a height of 7.5 centimeters.
3. Find the area of a trapezoid with a height of
9.3 inches and bases of 7.2 inches and 10.1 inches.
4. Find the volume of a rectangular solid with
dimensions of 8.5 meters, 10.3 meters, and
12.7 meters.
D ⫺ 0.7 2
b
D
Water
original
(water used
⫽ ⫺ D ⴢ ⫺ E
left
volume
per day)
Under emergency conditions, the village estimates
that it will use about 61,000 cubic feet of water per
day. The majority of the council believe that building
the reservoir is a good idea if it will supply the city
with water for at least 10 days. Otherwise, they will
vote against the plan.
1. Find the volume of water that the reservoir
will hold. Express the result in scientific
notation.
2. Will the reservoir supply the village for
10 days?
3. Would you vote for the plan? Explain.
4. How much water could the village use per day if
the supply must last for two weeks?