Volume and Surface Area
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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

 

 

2.  Consider this problem that gives "hints" on what is needed to solve the problem.

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?

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

 

 

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?

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

 

 

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.

 

a.  Find AB
b.  Find AD
c.  Find the surface area of the cylinder.