The equation of a plane in space is x + 3y + 2z = 6

1. The equation of a plane in space is x + 3y + 2z = 6.

Accurately sketch the plane on the set of axes, showing all your calculations below.

The three planes of the axes and the plane you have sketched create a triangular pyramid. Find the volume of this pyramid, showing the formula you are using and all
calculations below.

Graded Assignment

Name:

MTH203B/204B: Geometry | Unit 7 | Lesson 4: Semester Test

Date:

Graded Assignment
Unit Test, Part 2
Answer the questions below. When you are finished, submit this test to your teacher by the due date for full credit.
(9 points)

1.

The equation of a plane in space is x + 3y + 2z = 6.

Score

a.)

Accurately sketch the plane on the set of axes, showing all your calculations
below.

b.)

The three planes of the axes and the plane you have sketched create a triangular pyramid. Find
the volume of this pyramid, showing the formula you are using and all
calculations below.

Answer:

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Page 1 of 4

Graded Assignment

MTH203B/204B: Geometry | Unit 7 | Lesson 4: Semester Test

(16 points)

2.

Study the diagram below:

Score

a.)

If D is a right angle and lines PN, FG, and BD are parallel to each other, prove
SPN SFG SBD .

b.)

Use the diagram to solve this practical problem:
A person who is 1.5 m tall casts a shadow of 8 m. The distance along the ground from the person (N)
to the flagpole (G) is 32 m, and the distance from the flagpole (G) to the building (D) is 200 m. Find
the height of the flagpole (FG) and the height of the building (BD), showing all calculations.

Answer:

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Copying or distributing without K12’s written consent is prohibited.

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Graded Assignment

MTH203B/204B: Geometry | Unit 7 | Lesson 4: Semester Test

(12 points)

3.

Given rectangles ABCD and PQRS, and given that rectangle ABCD is fully rotated about
line BC, answer the following questions.

a.)

Score

Describe the figure generated by the rectangle rotating about line BC.

b.)

About which line could you rotate rectangle PQRS to generate a figure that is similar to the first
solid?

c.)

What are the ratios of the surface areas and volumes of the solids generated from ABCD and
PQRS?

d.)

Are ABCD and PQRS golden rectangles? Why or why not?

Answer:

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Copying or distributing without K12’s written consent is prohibited.

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Graded Assignment

MTH203B/204B: Geometry | Unit 7 | Lesson 4: Semester Test

(23 points)

4.

The diameter of circle C is 18 cm. Chord AD is the same length as a radius. Use this
information, the diagram, and your experiences in geometry this semester to answer these
questions. (Use 3.14 .)
a.)

A

Score

What are the measures of angles BDA
and DBA?

b.)
D

What is the sine of angle DBA?

c.)

Find the length of arc AB to the nearest
hundredth.

C

d.)

B

F

E

How does the length of arc AD
compare to the length of arc AB?

e.)

If EF =

1
BD, then what is the degree
2

measure of arc EF?
Answer:

Your Score

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Copying or distributing without K12’s written consent is prohibited.

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