Analytic Geometry Test Review
Unit 3 – Circles and Volume
Name:
Date:
------------------------------------------------------------------------------------------------------------------------------------------FIVE RESPONSE PROBLEMS x 12 POINTS EACH = 60 POINTS TOTAL.
1
Two chords CH and RD intersect inside a circle at point S. Suppose the
measure of arc RH is 80 and the measure of arc CD is 70. ( 12 pts )
(A) Draw chord CR. What are the measures of ∠𝐶𝑅𝐷 and ∠𝑅𝐶𝐻?
Explain. ( 4 pts )
(B) What is the measure of ∠𝐶𝑆𝐷? Explain. ( 4 pts )
(C) What is the measure of ∠𝐷𝑆𝐻? Explain. ( 4 pts )
2
3
A silo is used to hold grain. One is built with a cylinder with
a height of 60 meters capped by a hemisphere with a radius
of 20 meters. The formula for the volume of a cylinder is
given by 𝑉 = 𝜋𝑟 2 ℎ and the formula for the volume of a
4
sphere is given by 𝑉 = 𝜋𝑟 3 . What is the approximate
3
volume of this silo to the nearest 100th of a meter? Show
work and label units. ( 12 pts )
Triangle TRI circumscribes a circle with center Q and points of
tangency C, L and E. Suppose the measure of arc CL is 133 and arc
CE is 101.
(A) Find the measure of A. Show all work. ( 4 pts )
(B)
Find the measure of B. Show all work. ( 4 pts )
(C)
Find the measure of C. Show all work. ( 4 pts )
Analytic Geometry Test Review
Unit 3 – Circles and Volume
4
Name:
Date:
Quadrilateral PBLA is inscribed in circle O.
(A) What can be said about the sum of ∠𝑃 and ∠𝐿? Explain. ( 4 pts )
(B)
Suppose the measure of ∠𝑃 is 102. What should be the numerical
measures of ∠𝐿, arc BLA, and arc APB? Explain. ( 4 pts )
∠𝐿 ?
(C)
arc APB ?
Suppose the measure of ∠𝐴 is 77. What should be the numerical measures
of ∠𝐵, arc PBL, and arc PAL? Explain. ( 4 pts )
∠𝐿 ?
5
arc BLA ?

arc PBL ?
arc PAL ?
A rectangular harbor is located in a lagoon. The bow (front end) of
a canoe is tied to a corner of the harbor by a cable that is 15 feet
long as shown. The circular region shows the section of the lagoon
in which the bow of the canoe can maneuver.
(A) What should be the approximate area, in square feet, in
which the bow of the canoe can move? Show work and
label units. Round answers to the nearest 100th. ( 6 pts )
(B)
If the 15 foot long rope is replaced with a rope that is 20
feet long, then how will the area in which the bow can
move change? Show work and label units. Round answers
to the nearest 100th. ( 6 pts )
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