Geometric Topics
Bittinger:
p. 251: 59, 65, 85
p. 275: 19 Coming Maybe
Dr. Robert J. Rapalje
Seminole State College of Florida
Sanford, FL 32773
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Geometric Topics, with
detailed explanations, examples, exercises, and answers, select from the
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Metric System
Theorem of Pythagoras
Perimeters,
Areas, and Volumes
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P. 251:
59.
Find
the area between two circles. You must know that area of a circle is
A =
π
r
2 .
Solution: Outer Area radius = r ;
Area = π
r
2
Inner Area radius = 5; Area =
π
5
2
=
25π
Outer Area Inner Area
π
r
2
25π
65.
An 8
ft-wide round hot tub is installed in a patio measuring z ft by z ft.
Find a polynomial for the remaining area of the pool. You
must know that
area
of a circle is A =
π
r
2 ,
and area of a square is
A =
s
2.
Solution: Outer Area is a Square, side = z ;
Area = z
2
Inner Area is a Circle, Diameter = 8 ft, so Radius = 4 ft ; Area
= π
4
2
=
16π
Outer Area Inner Area
z
2
16π
sq. ft.
85.
Find
the surface area of a box! You must know that
box
consists of six faces
that are actually rectangles.
Each face, A =
LW
You must add up the 6
faces of the rectangular box. There will be 3 pairs of faces.
Solution: First face: Top and bottom = 3w +
3w = 6w
Second face: Sides
= 7*3 + 7*3 = 42
Third face:
Sides
= 7w + 7w = 14w
Total Surface area = 6w +
42 + 14w
= 20w + 42.
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