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Geometry / Mr. Hansen |
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Name:
__________________________________ |
Test
on Chapter 12, Portion 2
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Instructions and Scoring. Please read carefully before you begin. Check (þ) each item as you read it (1 pt. each). ¨
Do not discuss
this test with anyone except Mr. Hansen until the answers are posted on the
Web. ¨
It is OK now to
discuss yesterday’s test with
anyone you wish. ¨
There will be a
1-point deduction for each unnecessary disturbance during the test: speaking
out of turn, asking a question that has already been answered, etc. If you
have a question, please raise your hand and keep working until I spot you.
This may take a minute. Please do not call out my name, since that creates
unnecessary noise. If you see a typographical error, please mark it clearly
for extra credit. If you finish early, please leave quietly and
unobtrusively. ¨
No calculator
is permitted. ¨
There is a
homework assignment on the Web for Tuesday. ¨
This portion is
worth 50 points. Yesterday’s portion was also worth 50 points. The higher of
the two will be doubled. |
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Part I. |
Free Response. Show your work. Answers without clear, readable work will not earn
full credit even if they are correct. Units of measure are also required for
full credit. |
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1. |
The diameter of the sun is
approximately 800,000 miles, or approximately 1,300,000 km. Using rough estimation techniques, develop
an approximate figure for the volume of the sun. (For example, you may round p to 3, you may round 8 up to 10, and you may round
1.3 to 1.) Show your work. |
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2. |
The earth’s diameter is
approximately 1/100 that of the sun (8000 miles, or about 13,000 km). Estimate
the volume of the earth, not as a number, but as a fraction of the volume of
the sun. For example, if your answer is 1/1000th, you would write “1/1000” as
your answer, not an answer in mi3 or km3. Hint: Although you can do this by
computing a new answer and comparing it to #1, there is a much faster
shortcut that you are free to use. Show your work. |
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3.(a) |
Sketch a right circular cone
whose height is 8 cm and whose radius is 6 cm. Then show the lower frustum of
height 4 cm that is within the large cone. Your marked-up diagram is worth
half credit. Make it large enough to fill most of the space below. |
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(b) |
Compute the volume of the
frustum. |
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(c) |
Compute the total surface
area of the frustum. |
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4. |
Compute the volume and
total surface area of a right circular cylinder whose diameter is 8 inches
and whose diagonal (measured from far corner to far corner) is 10 inches. A
sketch is on the board, and you should feel free to copy it. |