Geometry
Unit 9 Modeling and Design – Review
Name ______________________________________
Find the surface area and volume of each figure.
1)
Surface Area Work:
Volume Work:
2)
Surface Area Work:
Volume Work:
3) Hemisphere (half a sphere)
Surface Area Work:
Volume Work:
4) Half a cylinder
Surface Area Work:
Volume Work:
Surface Area Work:
5) Hexagonal Prism
Volume Work:
Surface Area Work:
6) Sphere
Volume Work:
Surface Area Work:
7)
Volume Work:
Surface Area Work:
8)
Volume Work:
9)
Surface Area Work:
Volume Work:
10) You are tiling a 20 foot by 12 foot floor (shown below). You must fill the floor completely with one type of tile.
You have two types of tiles to choose from:
(Option 1) Right triangles that are 2 feet wide by 6 feet tall and cost $3.00
-OR(Option 2) Right triangles that are 4 feet wide by 4 feet tall and cost $3.50
a) Draw the tiling design for each type using the floor templates below:
(1)
(2)
b) Based on how many tiles are used in each design and the cost per tile, which option is the cheapest?
c) What is the cost per square foot for each type of tile? Which type of tile is the cheapest per square foot?
d) Do your answers for parts b) and c) agree? Explain why this makes sense.
11) The state of Colorado ranks 8th in the United States in terms of area. Its area is approximately 104,093 square
miles. Currently, there are approximately 5.2 million people living in Colorado.
a) What is the current population density of Colorado…
In square miles per person(to four decimal places)?
In square feet per person?
b) If 1 million additional people move to Colorado over the next 10 years, what will its population density be 10 years
from now…
In square miles per person (to four decimal places)?
In square feet per person?
12) Four soda cans are packaged so that they fit perfectly in a box as shown below. Each can has a diameter of 2.1
inches and a height of 4.1 inches.
a) What is the total volume of the box?
b) What is the total volume of the four cans?
c) What percentage of the box of cans is empty space?
1. SA 1568
Vol 4352
2. SA 644π = 2023.19 Vol 1862π = 5849.65
3. SA 27π = 84.82
Vol 18π = 56.55
4. SA 1363.27
Vol 2950.74
5. SA 323.14
Vol 415.69
6. SA 400π = 1256.64 Vol 1333.3π = 4188.79
7. SA 1046
Vol = 2244
8. SA 3614.8
Vol 11000
9. SA 270π = 848.23 Vol 550π = 1727.88
10. a) see drawing
b) (1) $120 (2) $105 Option 2
d) Yes; answers may vary
11. a) 0.0200 sq mi per person; 558,066.59 sq ft per person
b) 0.0168 sq mi per person; 468,055.85 sq ft per person
12. a) 72.32 in3
b) 56.80 in3
c) 21.46%
c) (1) $0.50 per sq ft (2) $0.44 per sq ft Option 2