Section 5'10 Geometry Applications: Circles and Cylinders

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Section 5.10 Geometry Applications Circles and
Cylinders
CIRCLES Radius (r) distance from the center
to the edge of circle Diameter (d) distance
from edge to edge through the center
d 2r or r p pi 3.14
Circumference (perimeter) distance around
the edge of the circle C 2 p r or p d
Area of a Circle A p r 2
2

• Find the diameter of a circle with radius 7
  inches.
• 2. Find the radius of a circle with diameter
  22 centimeters.

d 2 ( 7 in )
d 14 in
d 2r
d 2r
( 22 cm ) 2 r
11cm r
3

• 3. Find the area and circumference of a circle
  with radius 10 feet.
• 3. Find the area and circumference of a circle
  with radius 10 feet.

A p r 2
A p ( 10 ) 2
A (3.14) (100)
A 314 ft2
C 2 p r
C 2 p ( 10 )
C 2 (3.14) (10)
C 62.8 ft
4
Use your calculator on the following problems and
round to the nearest hundredth 4. a. Find the
circumference. b. Find the area.
C 2 p r
C 2 (3.14) ( 3 )
3 cm
C 18.84 cm
A p r 2
C (3.14) ( 3 ) 2
A 28.26 cm2
C (3.14) 9
5
Use your calculator on the following problems and
round to the nearest hundredth 5. a. Find the
circumference. b. Find the area.
C p d
C (3.14) ( 10 )
10 in
C 31.4 in
A p r 2
A (3.14) ( 5 ) 2
A 78.5 in2
A (3.14) 25
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Volume of a Cylinder V p r 2 h h
6. Find the volume
V p r 2 h
5 m
V ( 3.14 ) ( 5 ) 2 ( 11 )
11 m
V ( 3.14 ) ( 25 ) ( 11 )
V 863.5 m3
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7. Find the volume of a cylinder with radius 5
m, and height 7 m.
V p r 2 h
V ( 3.14 ) ( 5 ) 2 ( 7 )
V ( 3.14 ) ( 25 ) ( 7 )
V 549.5 m3
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8. Find the volume of a cylinder with diameter 1
in, and height 14 in.
V p r 2 h
V ( 3.14 ) ( 0.5 ) 2 ( 14 )
V ( 3.14 ) ( 0.25 ) ( 14 )
V 10.99 in3
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9. a. Find the perimeter.
P ½ C d
10 cm
P ½ (p d) d
P ½ (3.14 10) (10)
P (0.5) (31.4) (10)
P 25.7 cm
b. Find the area.
Area of semicircle ½ (p r 2 )
Area of semicircle ½ (3.14 5 2 )
Area of semicircle 0.5 (3.14 25 )
Area of semicircle 39.25 cm 2
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10. a. Find the perimeter.
P ½ C 3 sides of rectangle
P ½ (p d) 2l w
22cm 12 cm
P ½ (3.14 12) 2(22) 12
P (0.5) (37.68) 44 12
P 18.84 44 12
P 74.84 cm
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10. b. Find the area.
A ½ Circle rectangle
A ½ (p r 2) l w
22cm 12 cm
A ½ (3.14 6 2 ) ( 22 )( 12 )
A (0.5) (3.14 36) 264
A 56.52 264
A 320.52 cm2
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11. The radius of the moon is approximately
1,100 miles. Find the circumference of the moon
around its equator.
C 2 p r
C 2 p ( 1,100 )
C 2 (3.14) ( 1,100 )
C 6908 miles
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12. An earthquake was felt by people 1000 miles
away from the epicenter. How much area was
affected by the quake?
A p r 2
A p ( 1,000 ) 2
A (3.14) ( 1,000,000 )
A 3,140,000 mi 2
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13. Mark wanted to buy a pair of walkie-talkies.
One model had a range of 3 miles and the other
(much cheaper) model had a range of 2 miles.
What is the difference in the area covered by
the 3-mile and 2-mile models?
3-mile coverage
2-mile coverage
A p r 2
A p r 2
A p ( 3 ) 2
A p ( 2 ) 2
A 3.14 9
A 3.14 4
28.26 mi 2
12.56 mi 2
15.7 mi2
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Sec 5.10 Circles, cylinders and cubes (Do not
do Surface Area) Pg. 395 1 17 odd, 21
29 odd, 33 39 odd, 43 49 odd, 53, 55, 4,
8, 12, 16, 28, 44, 50, 56
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Section 6.1 Ratios Ratio comparison of the
same type of measurements. Write answers as
proper or improper fractions (no decimals or
mixed numbers).
If a and b are any two numbers, then the ratio
of a to b is or ab
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Write the following ratios as fractions in lowest
terms
1. 12 to 64
2.
18
3.
19
4. 6.4 to 0.8
20
5. 0.8 meters to 0.6 meters
21
6. 125 to 2000
7.
22
3.
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Nutrition One cup of breakfast cereal was found
to contain the following nutrients in grams. Use
the chart to find the following ratios.
9. Water to protein.
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Nutrition One cup of breakfast cereal was found
to contain the following nutrients in grams. Use
the chart to find the following ratios.
10. Vitamins to minerals
25
11. Carbohydrates to protein.
12. Protein to vitamins and minerals.
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Find the ratio of the length of the longest to
the length of the shortest side.
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Find the ratio of the length of the longest to
the length of the shortest side.
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Sec 6.1 Ratios Pg. 427 1 27 odd, 35 47
odd, 12, 16, 18, 22, 44
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Section 6.2 Rates Ratio - comparison of like
measurements. Rate comparison of unlike
measurements. Write answers as whole numbers or
decimals and include appropriate units in the
answer. Words often used to represent rates
in for on per from
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Write each rate as a fraction in lowest terms.
1. 120 miles in 3 hours. 2. 108 for 6
visits 3. 210 miles on 12 gallons 4. 124
students in 4 classes
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5. A train travels 360 miles in 5 hours.
Find the rate in miles per hour.
72 miles per hour
6. A 22-gallon drum is filled in 3 minutes.
Find the rate in gallons per minute.
7.3 gallons per minute
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7. The flow of water from a facet can fill a
3-gallon container in 15 seconds. Find the rate
in gallons per second. 8. In 6 hours an
airplane travels 4,200 kilometers. What is the
rate in kilometers per hour?
0.2 gallons per second
700 kilometers per hour
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Unit Rates the rate of two unlike measurements
with the denominator 1. Answers will be whole
numbers or decimals with appropriate units in the
answer and a denominator of one. Use your
calculator to answer the following questions. If
necessary, round to the hundredth. 9. A
2-liter bottle of root beer costs 1.25. Give the
unit price in cents per liter.
cents
62.5 cents per liter
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10. An 8-pound bag of dog food costs 10.12. A
25-pound bag of dog food costs 32.50. Give the
unit price in dollars per pound for each bag.
Which bag of dog food is the better buy?
25-pound bag
8-pound bag
1.265 per lb
1.3 per lb
The 8-pound bag of dog food is a better buy.
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11. A hybrid car travels 675.4 miles on 12
gallons of gas. What is the gas mileage?
54.032 mpg
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12. At the beginning of a trip the odometer of a
car read 32,567.1 miles. At the end of the trip
it read 32,741.8 miles. If the trip took 14
hours, what was the rate of the car in miles per
hour?
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Sec 6.2 Rates Pg. 435 1 45 eoo, 14, 20, 30,
36, 44