AnswersSS26 Math 3 S2 M3960OXCavalieri's Principle and Volume of Composite Figures

Cavalieri's Principle and Volume of Composite Figures — Cumulative exam Answers

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Triangle A B C is shown. Angle A B C is a right angle. Angle B C A is 22 degrees and angle C A B is 68 degrees.

Question illustration
A
cos(B)
B
sin(B)
C
cos(C)
D
tan(C)
2
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A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section.

Question illustration
A
21.2 m
B
27.5 m
C
32.5 m
D
38.2 m
3

Circle O is shown. Tangents B C and B A intersect at point B outside of the circle. The measure of the first arc formed is 146 degrees.

Question illustration
A
34°
B
45°
C
68°
D
73°
4

Heron’s formula: Area =

Question illustration
A
square units
Option A
B
square units
Option B
C
square units
Option C
D
square units
Option D
5

Question text not available

A
Circle C is shown. Line segment A C is a radius with length 6 centimeters.
Option A
B
Circle C is shown. Line segment A C is a radius with length 7 centimeters.
Option B
C
Circle C is shown. Line segment A C is a radius with length 8 centimeters.
Option C
D
Circle C is shown. Line segment A C is a radius with length 9 centimeters.
Option D
6

What is the area of triangle ABC? Round to the nearest square unit.

Question illustration
A
8 square units
B
15 square units
C
33 square units
D
618 square units
7

Two chords intersect at a point inside a circle that is not the center of the circle. Which statement must be true?

A
The measures of each pair of opposite arcs sum to 180°.
B
Each angle measure is equal to the measure of the arc it intercepts.
C
The sum of the measures of each pair of vertical angles is equal to the sum of the measures of the intercepted arcs.
D
Each arc measure is equal to one-half the sum of the vertical angles that intercept the arc.
8

Line EF is tangent to circle G at point A.

Question illustration
A
90°
B
95°
C
190°
D
195°
9

Triangle J K L is shown. Angle K L J is a right angle. The length of hypotenuse K J is 10.9 centimeters and the length of L J is 8.9 centimeters. Angle L K J is x.

Question illustration
A
cos−1 = x
Option A
B
cos−1 = x
Option B
C
sin−1 = x
Option C
D
sin−1 = x
Option D
10

Given: RT ≅ TV and ST ≅ TUProve: RSVU is a parallelogram. Statements Reasons1.RT ≅ TV; ST ≅ TU1.given2.∠RTS and ∠VTU are vert. ∠s;∠RTU and ∠VTS are vert. ∠s2.definition of vertical angles3.∠RTS ≅ ∠VTU;∠RTU ≅ ∠VTS3.vertical angles are congruent4.?4.SAS congruency theorem5.∠VRS ≅ ∠RVU; ∠USR ≅ ∠SUV; ∠VRU ≅ ∠RVS; ∠RUS ≅ ∠USV5.CPCTC6.∠VRS and ∠RVU, ∠USR and ∠SUV, ∠VRU and ∠RVS, ∠RUS and ∠USV are each a pair of alternate interior angles6.definition of alternate interior angles7.RS ∥ UV and RU ∥ SV7.converse of the parallelogram diagonal theorem8.RSVU is a parallelogram8.definition of parallelogramWhat is the missing statement in step 4?

Question illustration
A
△RTS ≅ △VTU and △RTU ≅ △VTS
B
△RTS ≅ △RVS and △RTU ≅ △STV
C
△VRS ≅ △VRU and △USR ≅ △USV
D
△VUR ≅ △VUS and △UVS ≅ △SRU
11

Triangles A B C and X Y Z are shown. Angles A B C and X Y Z are right angles. Angles B A C and Y X Z are congruent. The length of A B is 5, the length of A C is 13, and the length of B C is 12.

Question illustration
A
Five-thirteenths
Option A
B
Five-twelfths
Option B
C
Twelve-thirteenths
Option C
D
Twelve-fifths
Option D
12

A corner of a rectangle is cut, creating a trapezoid.

Question illustration
A
105o
B
115o
C
125o
D
135o
13

A solid right pyramid has a square base with an edge length of s units and a height of h units.

Question illustration
A
s2h units3
Option A
B
s2h units3
Option B
C
s2h units3
D
3s2h units3
14

The table shows information about Town A in Illinois and Town B in Florida.

Question illustration
A
Town B has the same population as Town A.
B
Town B has a greater population than Town A.
C
Town B has a population of approximately 5,138.
D
Town B has a population of approximately 37,530.
15

On a coordinate plane, parallelogram P Q R S is shown. Point P is at (5, 1), point Q is at (6, 4), point R is at (3, 10), and point S is at (2, 7).

Question illustration
A
The slopes of SP and RQ are both –2 and SP = RQ = .
Option A
B
The slopes of RS and QP are both 3 and SP = RQ = .
Option B
C
The midpoint of RP is and the slope of RP is .
Option C
D
The midpoint of SQ is and SQ = 5.
Option D
16

Arc QVT measures 156°.

Question illustration
A
Angles QRT and QST both measure 78°.
B
Angles QRT and QST both measure 156°.
C
Angle QRT measures 78° and angle QST measures 102°.
D
Angle QRT measures 156° and angle QST measures 24°.
17

An oblique square prism is shown.

Question illustration
A
x(x – 2) cubic units
B
x(x +1) cubic units
C
x2(x – 2) cubic units
D
x2(x +1) cubic units
18

Triangle Q R S is shown. Angle Q R S is a right angle. Angle R S Q is 30 degrees and angle S Q R is 60 degrees. The length of R S is 5 StartRoot 3 EndRoot, the length of S Q is 10, and the length of R Q is 5.

Question illustration
A
StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Option A
B
One-half
Option B
C
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option C
D
StartFraction 2 Over 1 EndFraction
Option D
19

All tangents to the circle are congruent and form a square. The perimeter of square ACEG is 24 cm.

Question illustration
A
2 cm
B
3 cm
C
6 cm
D
8 cm
20

Parallelogram L M N O is shown. Angle N is (2 x) degrees and angle L is (3 x minus 20) degrees.

Question illustration
A
20°
B
30°
C
40°
D
50°

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