Solving Equations Examples And Worksheet Page 11
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14A59
Appendix A.5
Solving Equations
Common Formulas
The following geometric formulas are used at various times throughout this course. For
your convenience, some of these formulas along with several others are also provided
on the inside cover of this text.
Common Formulas for Area A, Perimeter P, Circumference C, and Volume V
Rectangle
Circle
Triangle
Rectangular Solid
Circular Cylinder
Sphere
1
4
2
2
3
A
lw
A
r
A
bh
V
lwh
V
r
h
V
r
2
3
P
2l
2w
C
2 r
P
a
b
c
r
h
r
w
a
c
r
h
l
w
l
h
b
Example 15
Using a Geometric Formula
3
A cylindrical can has a volume of 200 cubic centimeters
cm
and a radius of
4 cm
4 centimeters (cm), as shown in Figure A.13. Find the height of the can.
Solution
h
2
The formula for the volume of a cylinder is
V
r
h.
To find the height of the can,
solve for
h.
V
h
A.13
FIGURE
2
r
Then, using
V
200
and
r
4,
find the height.
200
h
Substitute 200 for V and 4 for r.
2
4
200
Simplify denominator.
16
3.98
Use a calculator.
Because the value of
h
was rounded in the solution, a check of the solution will not
result in an equality. If the solution is valid, the expressions on each side of the equal
sign will be approximately equal to each other.
2
V
r
h
Write original equation.
?
2
200
4
3.98
Substitute 200 for
V,
4 for
r,
and 3.98 for
h.
✓
200
200.06
Solution checks.
You can also use unit analysis to check that your answer is reasonable.
3
200 cm
3.98 cm
2
16 cm
Now try Exercise 157.
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