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Let's look
at some hints and strategies for dealing with three dimensional
problems. |
Answers will use
 =
3.141592654, the full calculator entry on the TI-83+.
(Answers will be rounded to
the nearest hundredth unless otherwise stated.)
1. Consider this problem where radius is needed but not
given:
a.
Find the volume of this cylinder.
b.
Find the surface area if this cylinder represents a can
which has no lids. |
a.
When
a formula needs a radius,
be sure that you are
working with the radius
and not the diameter. In
this problem 12" is the diameter (radius = 6").
b. You may need to
amend your formula
to fit a particular situation.
The surface area formula for a cylinder is
This formula includes the
areas of the top and bottom (which are 2 circles). If
the top and bottom are NOT to be considered, the formula
will be
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2. Consider this problem that gives "hints" on
what is needed to solve the problem. |
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A
die is a cube molded from hard plastic. The edge
of a typical die measures 0.62 inches. Dice are
usually produced in a mold which holds 100 die at one
time. To the nearest cubic inch, how much plastic
is needed to fill this large mold? |
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When
working with word problems, be sure to read carefully to
determine what the question wants you to find.
This question clearly
involves volume since it states "to the nearest cubic inch."
Also, the answer must be for 100 dice, not 1 die.
Volume
of one die = lwh = (.62)(.62)(.62) =0.238 cubic
inches
For 100 dice = (0.238)(100) = 23.8 = 24
cubic inches |
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3. |
Consider this problem with different units of measure.
A
concrete truck arrives at a job site holding 7.8 cubic
yards of concrete. If the patio being constructed
is 18 feet across and 4 inches thick, how long, to the
nearest foot, will the
patio be if constructed from the amount of concrete on
the truck? |
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Always
read carefully to determine if all of the measurements
within a problem are expressed
in the same units.
This problem deals with inches, feet and cubic yards.
1 cubic
yard = 27 cubic feet
(think of a cube 1 yd. x 1 yd. x 1 yd. which is also
3 ft. x 3 ft. x 3 ft.)
7.8 cubic
yards x 27 = 210.6 cubic feet
4 inches = 0.333 ft.
V = lwh
210.6 = (l)(18)(0.333)
length = 35.1 feet
= 35 feet
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4. Consider this problem
that requires visualization. |
When
dealing with surface area it is often helpful to imagine
the figure cut apart
(called a net).
In this example, imagine
cutting off the top and bottom of the cylinder and then
slicing the remaining shape and flattening it out.
a.
AB = 12"
b.
AD = the length around the "edge" of the cylinder (which is
a circle) = circumference of a circle
c.
Surface area
= 294.12 sq. in.
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a.
Find AB
b. Find AD
c. Find the
surface area of the cylinder. |
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