Circles & Volume: Part 1 Unit Test Review

Circle P has a circumference of approximately 75 inches. What is the approximate length of the radius, r? Use 3.14 for pi. Round to the nearest inch. 12 inches 24 inches 38 inches 46 inches

12 inches

In circle V, angle WXZ measures 30°. Line segments WV, XV, ZV, and YV are radii of circle V. What is the measure of segment WUX in circle V? 60° 90° 120° 150°

120°

The measure of minor arc JL is 60°. What is the measure of angle JKL? 110° 120° 130° 140°

120°

In circle Z, what is m∠2? 70° 133° 140° 147°

140°

What is the measure of segment EAB in circle F? 72° 92° 148° 200°

148°

What is the measure of minor arc segment EG? 17° 75° 149° 211°

149°

Points N and R both lie on circle O. Line segment RQ is tangent to the circle at point R. What is the perimeter of triangle RON? 10.0 units 15.0 units 18.7 units 23.7 units

15.0 units

What is the measure of angle COA? 140° 150° 160° 170°

160°

In circle A, ∠BAE ≅ ∠DAE. What is the value of x? 14 17 27 34

17

Consider circle T with radius 24 in. and θ = 5π/6 radians. What is the length of minor arc SV? 20π in. 28π in. 40π in. 63π in.

20π in.

Line segment GJ is a diameter of circle L. Angle K measures (4x + 6)°. What is the value of x? 21 24 32 44

21

What is the measure of segment CED? 106° 108° 148° 212°

212°

In circle O, segment AC and segment BE are diameters. The measure of arc DC is 50°. What is the measure of segment EBC? 40° 90° 140° 220°

220°

Line segment ON is perpendicular to line segment ML. Line segment OM = 13 units in length, line segment PN = 8 units in length. What is the length of chord ML? 20 units 24 units 26 units 30 units

24 units

In circle O, segment AE and segment FC are diameters. Arc ED measures 17°. What is the measure of segment EFC? 107° 180° 253° 270°

253°

In circle M, diameters JL and HK each measure 16 centimeters. What is the approximate length of minor arc JH? Round to the nearest tenth of a centimeter. 3.5 cm 6.9 cm 21.6 cm 46.8 cm

3.5 cm

In circle Y, what is m∠1? 6° 25° 31° 37°

31°

Points E, F, and D are located on circle C. The measure of arc ED is 68°. What is the measure of angle EFD? 34° 68° 112° 132°

34°

In the diagram of circle C, what is the measure of ∠1? 17° 35° 70° 71°

35°

The measure of central angle YCZ is 80 degrees. What is the sum of the areas of the two shaded sectors? 18π units^2 36π units^2 45π units^2 81π units^2

36π units^2

Point G is the center of the small circle. Point X is the center of the large circle. Points G, H, and X are on line segment GX. What would be the area of a new circle that has line segment GX as its diameter? 16π cm^2 36π cm^2 49π cm^2 98π cm^2

49π cm^2

In the diagram of circle O, what is the measure of angle ABC? 27° 54° 108° 120°

54°

Segment QR is tangent to circle P at point Q. What is the approximate length of RP? Round to the nearest tenth. 5.6 units 6.1 units 8.3 units 9.8 units

6.1 units

The measure of central angle RST is radians. What is the area of the shaded sector? 4π units^2 8π units^2 16π units^2 20π units^2

8π units^2

Circle T has diameters RP and QS. The measure of ∠RTQ is 12° less than the measure of ∠RTS. What is the measure of segment QP? 78° 84° 88° 96°

96°

Points N, P, and R all lie on circle O. Arc PR measures 120°. How does the measure of angle RNQ relate to the measure of arc PR? Angle RNQ is equal in measure to arc PR. Angle RNQ is half the measure of arc PR. Angle RNQ is twice the measure of arc PR. Angle RNQ is four times the measure of arc PR.

Angle RNQ is equal in measure to arc PR.

A circular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet. What is the approximate area of the path alone? Use 3.14 for pi. 172.70 ft^2 178.98 ft^2 200.96 ft^2 379.94 ft^2

NOT 379.94 ft^2 (most likely 178.98 ft^2)

Segment QR is tangent to circle P at point Q. What is the measure of angle R? 37° 53° 90° 97°

NOT 90° (most likely: 37°)

In each circle below, a 50° angle with a vertex at the center of the circle is drawn. How are minor arc lengths CD and EF related? They are the same because the central angle measure is the same. The arc lengths are proportional: CD = 2EF. The arc lengths are proportional: CD = 4EF. The arc lengths are proportional: CD = 6EF.

The arc lengths are proportional: CD = 4EF.

Which statements are true regarding the area of circle D? Select two options. The area of the circle depends on the square of the radius. The area of circle D is 36π cm^2 The area of circle D is 324π cm^2 The area of the circle depends on the square of pi. The area of the circle depends on the central angle.

The area of the circle depends on the square of the radius. The area of circle D is 324π cm^2

Given: Circle O with diameter LN and inscribed angle LMN Prove: is a right angle. What is the missing reason in step 5? Statements Reasons 1. circle O has diameter LN and 1. given inscribed angle LMN 2. segment LKN is a semicircle 2. diameter Θ divides into 2 . semicircles 3. circle O measures 360° 3. measure of a circle is 360° 4. m LKN = 180° 4. definition of semicircle 5. m∠LMN = 90° 5. ? 6. ∠LMN is a right angle 6. definition of right angle HL theorem inscribed angle theorem diagonals of a rhombus are perpendicular. angles formed by a tangent and a chord is half the measure of the intercepted arc.

inscribed angle theorem

An arc on a circle measures 85°. The measure of the central angle, in radians, is within which range? 0 to π/2 radians π/2 to π radians π to 3π/2 radians 3π/2 to π radians

0 to π/2 radians

In circle O, what is mAE? 84° 96° 120° 168°

120°

Circle O has a circumference of approximately 44 in. What is the approximate length of the diameter, d? 7 in. 14 in. 22 in. 44 in.

14 in.

In circle T, ∠PTQ ≅ ∠RTS. What is the length of segment PQ? 3 units 4 units 6 units 7 units

4 units

Line segment XY is tangent to circle Z at point U. If the measure of segment UV is 84°, what is the measure of angle YUV ? 42° 84° 96° 168°

42°

The smallest of the three circles with center D has a radius of 8 inches and CB = BA = 4 inches. What is the sum of the areas of all three circles? 80π in.^2 96π in.^2 208π in.^2 464π in.^2

464π in.^2

Fiona draws a circle with a diameter of 14 meters. What is the area of Fiona's circle? 7π m^2 14π m^2 28π m^2 49π m^2

49π m^2

What is the measure of arc ECF in circle G? 52° 98° 158° 177°

98°

In circle D, which is a secant? segment EF segment DC ray AB line GH

line GH

Angle BCD is a circumscribed angle of circle A. Angle BCA measures 40°. What is the measure of minor arc BD? 40° 50° 80° 100°

100°

In the diagram of circle P, m∠XYZ is 72°. What is the value of x? 108° 144° 216° 252°

108°

Points E, F, and D are located on circle C. The measure of arc ED is 108°. What is the measure of angle ECD? 54° 72° 108° 126°

108°

Segment FH is tangent to circle G at point F. What is the length of the radius, r? 10 units 12 units 20 units 24 units

12 units

Circle Q has a circumference of approximately 50 centimeters. What is the approximate length of the diameter, d? Use 3.14 for pi. Round to the nearest tenth of a centimeter. 4.0 centimeters 8.0 centimeters 15.9 centimeters 31.8 centimeters

15.9 centimeters

Which statements are true about circle Q? Select three options. The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8. The area of the shaded sector is 4 units^2. The area of the shaded sector depends on the length of the radius. The area of the shaded sector depends on the area of the circle. The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the area of the circle.

NOT COMBO: The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8. The area of the shaded sector depends on the length of the radius. The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the area of the circle.

What is true regarding two adjacent arcs created by two intersecting diameters? They always have equal measures. The difference of their measures is 90°. The sum of their measures is 180°. Their measures cannot be equal.

The sum of their measures is 180°.

What does segment CDE describe? a minor arc a major arc a semicircle a chord

a major arc

Given: quadrilateral ABCD inscribed in a circle Prove: ∠A and ∠C are supplementary, ∠B and ∠D are supplementary Let the measure of segment BCD = a°. Because segment BCD and segment BAD form a circle, and a circle measures 360°, the measure of segment BAD is 360 - a°. Because of the __________ theorem, m∠A = a/2 degrees and m∠C = 360-a/2 degrees. The sum of the measures of angles A and C is (a/2 + 360-a/2) degrees, which is equal to 360°/2, or 180°. Therefore, angles A and C are supplementary because their measures add up to 180°. Angles B and D are supplementary because the sum of the measures of the angles in a quadrilateral is 360°. m∠A + m∠C + m∠B + m∠D = 360°, and using substitution, 180° + m∠B + m∠D = 360°, so m∠B + m∠D = 180°. What is the missing information in the paragraph proof? inscribed angle polygon interior angle sum quadrilateral angle sum angle bisector

inscribed angle

Which equation can be used to find the measure of segment EHG? mEHG + 80 + 35 = 180 mEHG + 80 + 35 = 360 mEHG - 80 - 35 = 360 mEHG - 80 - 35 = 180

mEHG + 80 + 35 = 360

Which equation is correct regarding the measure of ∠MNP? m∠MNP = 1/2(x - y) m∠MNP = 1/2(x + y) m∠MNP = 1/2(z + y) m∠MNP = 1/2(z - y)

m∠MNP = 1/2(x - y)

Which equation is correct regarding the diagram of circle O? m∠XZY = 1/2(a + b) m∠XZY = 1/2(a - b) m∠XOY = 1/2(a + b) m∠XOY = 1/2(a - b)

m∠XZY = 1/2(a - b)

In the diagram below, Θ is measured in radians. Which equation represents the relationship between the radius, r, and arc length, s? s = Θ · r r = Θ · s s = Θ + r r = Θ + s

s = Θ · r

Which arc is congruent to segment EH? segment GH segment FH segment GE segment FG

segment GE

Given: Circle M with inscribed and congruent radii JM and ML Prove: m = What is the missing reason in step 8? Statements Reasons 1. circle M with inscribed ∠KJL and 1. given congruent radii JM and ML 2. △JML is isosceles 2. isos. △s have two . congruent sides 3. m∠MJL = m∠MLJ 3. base ∠s of isos. △are ≅ and . have = measures 4. m∠MJL + m∠MLJ = 2(m∠MJL) 4.substitution property 5. m∠KML = m∠MJL + m∠MLJ 5.measure of ext. ∠ equals . sum of measures of remote . int. ∠s of a △ 6. m∠KML = 2(m∠MJL) 6. substitution property 7. mKL = m∠KML 7. central ∠ of △ and . intercepted arc have same . measure 8. mKL = 2(m∠MJL) 8. ? 9. 1/2(mKL) = m∠MJL 9. multiplication property of . equality reflexive property substitution property base angles theorem second corollary to the inscribed angles theorem

substitution property

Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD. Which statements about the arcs and angles are true? Select three options. ∠EFD ≅ ∠EGD ∠EGD ≅ ∠ECD segment ED ≅ segment FD mEF = 60° mFD = 120°

NOT COMBO: ∠EFD ≅ ∠EGD segment ED ≅ segment FD mEF = 60°

A secant and a tangent meet at a 90° angle outside the circle. What must be the difference between the measures of the intercepted arcs? 45° 90° 180° 270°

180°

In circle G, r = 3 units. Maria draws a circle with double the area of circle G. What is the area of Maria's circle? 6π units^2 9π units^2 12π units^2 18π units^2

18π units^2

Line EF is tangent to circle G at point A. If the measure of angle CAE is 95°, what is the measure of segment CBA? 90° 95° 190° 195°

190°

Angle BAC measures 56°. What is the measure of angle BDC? 28° 34° 56° 112°

56°

Circle X with a radius of 6 units and circle Y with a radius of 2 units are shown. Which steps would prove the circles similar? Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 4. Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 4. Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3. Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 3.

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.

Major arc JL measures 300°. Which describes triangle JLM? right obtuse scalene equilateral

equilateral

Which equation is correct regarding the measure of ∠1? m∠1 = 1/2(a - c) m∠1 = 1/2(a + c) m∠1 = 1/2(b - d) m∠1 = 1/2(b + d)

m∠1 = 1/2(b - d)

Arc CD is 1/4 of the circumference of a circle. What is the radian measure of the central angle? π/4 radians π/2 radians 2π radians 4π radians

π/2 radians

Arc AB is 1/6 of the circumference of a circle. What is the radian measure of the central angle? π/6 π/3 2π/3 5π/6

π/3

In circle D, ∠EDH ≅ ∠EDG. What is the measure of segment EH? 114° 123° 228° 246°

123°

In circle O, SU is a diameter. What is mST? 100° 108° 130° 160°

130°

In circle O, segment AC and segment BD are diameters. What is mBC? 50° 80° 100° 130°

130°

In circle N, segment KL ≅ segment ML. What is the measure of segment JM? 77° 90° 132° 154°

132°

In the figure, angle ZYX is measured in degrees. The area of the shaded sector can be determined using the formula m∠ZXY/360°(πr^2). Which best explains the formula? The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector. The central angle measure of the sector divided by the total angle measure of a circle multiplied by the circumference of the circle will yield the area of the sector. The central angle measure of the sector multiplied by the area of the circle will yield the area of the sector. The central angle measure of the sector multiplied by the circumference of the circle will yield the area of the sector.

The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.