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Graded Assignment
MTH203B/204B Geometry | Unit 2 | Lesson 18: Surface Area and Volume Unit Test
Name:
Date:
Graded Assignment
Unit Test, Part 2
You are able to choose any two questions between Numbers 1, 2, and 4. You will skip one question
below, in other words (1,2,3 or 1,3,4 or 2,3,4). Note that question 3 is required. Credit will be given
for a total of three answers (39 points possible). You will not get credit for doing extra.
If this test is completed and submitted by March 26th you can earn 2 bonus points.
ouAnswer the questions below. When you are finished, submit this test to your teacher..
(12 points)
1. Jon started with a diagram like the one below and drew a three-dimensional figure by rotating
the circle 360? about line m.
Score
Nadia started with a diagram like the one shown below and drew a three-dimensional figure by rotating the
right triangle ABC 360? about line n.
a) Name the three-dimensional figure created by each person.
b) Nadia remarked that her figure has an infinite number of planes of symmetry. Jon gave a sly grin and
remarked that his figure has an infinite number plus one! After explaining the difference between his figure’s
planes of symmetry and hers, Jon convinces Nadia that his figure does have one more than hers. How might
Jon have explained this?
Answer:
a) Name Jon’s figure:
Name Nadia’s figure:
b)
Jon’s possible Explanation:
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Copying or distributing without K12’s written consent is prohibited.
Page 1 of 4
Graded Assignment
MTH203B/204B Geometry | Unit 2 | Lesson 18: Surface Area and Volume Unit Test
(12 points)
2. A triangular pyramid begins with these coordinates:
Score
P: (0, 5, 4)
Y: (¬Ė2, 7, 4)
R: (0, 7, 4)
A: (0, 7, 6)
The pyramid is then reflected over the xz-plane. The reflected image is then translated 3 units back, 2 units
left, and 4 units up. Determine the coordinates of that final image, following these steps:
a)
Write the general rule you use for the reflection.
b)
Show the results of your calculations for the reflection.
c)
Write the general rule you use for the translation. (Hint: Begin with the result of the rule for the
reflection.This translation happens to the reflection image of the original pyramid.)
d)
Show your calculations for the translation.
Answer all four parts:
a)
Reflection Rule:
b) Calculation Work and final Reflection coordinates:
c) Translation Rule from b):
d)
Translation Calculations and Coordinates:
© 2007 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 2 of 4
Graded Assignment
MTH203B/204B Geometry | Unit 2 | Lesson 18: Surface Area and Volume Unit Test
(15 points)
3. Required:
Score
Rectangle RECT is rotated 360¬į about the y-axis.
Find the surface area and volume of the resulting solid of revolution. Be sure to do the following:
Indicate the type of solid that was formed and its key dimensions.
State all formulas.
Show all substitutions and work.
Use appropriate units in your answers.
Answer:
a)
Solid Name and key dimensions:
b)
Formulas for SA:
Vol:
c)
Substitutions, work (computation), and answer with appropriate units
Surface Area:
Volume:
© 2007 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 3 of 4
Graded Assignment
MTH203B/204B Geometry | Unit 2 | Lesson 18: Surface Area and Volume Unit Test
(12 points)
4. A prism has total surface area of 360 m 2 and volume of 60 m3.
Score
If the length, width, and height are reduced to half (1/2) their original sizes, calculate the
following showing all of your computation.
a. the new surface area
b. the new volume
If the length, width, and height of the original are increased to triple (3) their original sizes, claculate following
showing all of your computation.
c.
the new surface area
d. the new volume
Show your calculations for all four parts.
Answer:
a) Computation and answer for New SA of reduced prism with appropriate units.
b)
Computation and answer for New Vol of reduced prism with appropriate units.
c) Computation and answer for New SA of enlarged prism with appropriate units.
d) Computation and answer for New Vol of enlarged prism with appropriate units.
Your Score
© 2007 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
___ of 39
Page 4 of 4
Math | Extended Problems: Reasoning | The Second Dimension
Extended Problems: Reasoning
The Second Dimension
Solve.
1. Chris is creating a triangular-shaped garden. He creates a scale drawing with coordinates A, B, and C to
represent each corner of the garden. Triangle ABC has vertices located at
A(4, 0), B(4, 3) and C(¬Ė3, 0).
(a) Draw the triangle that represents Chris’s garden. Use the formula for the area of a triangle to determine
the area of the garden in square units. Show your work.
(b) Chris knows that 1 unit is equivalent to 2 ft on his graph. Chris says that to calculate the area in square
feet, he can just double the area that he calculated in square units. Is Chris correct? Explain why or why
not.
(c) Chris decides to plant corn in one-third of his garden. Chris wants to plant only four corn plants in each
square foot of this section of the garden to ensure each plant has enough room to grow. How many corn
plants will he need? Show your work.
Math | Extended Problems: Reasoning | The Second Dimension
2. Sara and three of her friends use an Internet mapping application to map the location of each of their houses.
Sara¬ís house is located at (¬Ė2, ¬Ė5), Nate¬ís house is located at (¬Ė2, 2), Michelle¬ís house is located at (4, ¬Ė5),
and Joshua’s house is located at (x, y).
(a) Plot the three points representing Sara’s, Nate’s, and Michelle’s houses.
(b) The friends discover that the four houses are the vertices of a rectangle. What are the coordinates of
Joshua’s house? Explain.
(c) Joshua wants to know how far he would have to ride his bike on a trip from his house to Nate’s then to
Sarah’s, then to Michelle’s, and finally back home. Use the appropriate mathematical formula to
determine the distance in coordinate units that Joshua would have to ride. Show your work.
(d) Joshua knows that 1 unit on the graph represents 3 mi. He says he can multiply the perimeter of the
rectangle in units by 3 to calculate the perimeter in miles. Is Joshua correct? Explain why or why not.
Math | Extended Problems: Reasoning | The Second Dimension
3. The two points on the coordinate plane represent two corners of a large park.
(a) Reflect point A across the x-axis to create point A’. Reflect point B across the x-axis to create point B’.
What are the coordinates of point A’ and point B’ ? Explain.
(b) The park is a rectangle formed by all four points. One unit represents 0.5 mi. What is the area of the park
in square miles? Show your work.
Math | Extended Problems: Reasoning | The Second Dimension
4. Drew made a conjecture about the distance between two points on a coordinate plane. He said that if both
points have the same x-coordinates, then the distance between the two points is the distance between the
two y-coordinates. If both points have the same
y-coordinates, then the distance between the two points is the distance between the x-coordinates.
Is Drew correct? Explain.

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