2D Geometry Questions and Answers

1 PART 1 Point A In radians what is Point B In radians what is Point C Point B is at 300 Point D is at 45 In radians what is Point A In radians what is Point D Point D In radians what is Point E Point C Point B

Use the Hinge Theorem and its converse to describe the restrictions on the value of the variable 12 18 126 12 26 3x 2 18 Enter the correct inequality in the box Show Hints X

4 For problems a e use the diagram below K G 54 72 H a Which arc does ZKGJ intercept b Which angle intercepts GHJ c What is mZH d What is mJH e What is mZGJH f Which angles are supplementary

3 Write the equation of a circle in standard form with diameter AB Where A 7 5 and B 1 1 For full credit show your work Hint You need to find the midpoint of the diameter This is the center of the circle Then you need to find the distance between the midpoint and one of the endpoints This is the length of the radius Midpoint x x 2 2 Distance x x

1 A classmate insists that the value of x is 10 Write an equation to show that your classmate is wrong and solve for x 5 12

your answer to the nearest tenth b You find another soccer ball at the street with a radius of 16 Which soccer ball has the greatest volume Explain using mathematical evidence

4 Determine the volume of the sphere below Round to the nearest hundredth 12 yd

3 A globe of the Moon has a radius of 10 inches Find the volume of the globe Round to the nearest whole number

Yusef is purchasing a pi ata for his sister s birthday party He wants to buy the pi ata that can hold the most items so she can fill it up with lots of goodies Below are the shapes of the two pi atas he is considering buying Which one should Yusef purchase Why 13 in 7 in 16 in

1 A rectangular pyramid has a base with an area of 18 in If the altitude of the pyramid is 14 in what is the volume of the pyramid 3 a 18 in b 84 in 42 in C d 252 in 3

There are two triangles for which A 30 a 7 and b 10 The larger one has c and the smaller one has c Note You can earn partial credit on this problem

12 You have been hired to design a box rectangular prism with a volume of 24 m The height of the box must be 2 m a Create a table like the one below and fill in the blanks Use whole numbers for dimen sions 6 marks Length m 1 2 3 4 6 12 Width m Height m 2 2 2 2 2 2 Volume m 24 24 24 24 24 24 Surface Area m

2 The equation x 6x y2 6y 9 0 is an equation of a circle in expanded form Complete the square to find the center and radius and then write the equation of the circle in standard form To earn full credit you must show your work a center b radius c Equation

Which is the equation of a circle with diameter AB where A 5 4 and B 1 4 Select one O a x 2 2 y 25 O b x 2 2 y 5 O c x 5 2 y 4 100 O d x 5 2 y 4 10

Which of the following is the graph of x 2 y 1 9 Select one O a O b C O d 4 O y y ty 2 20 ty O 2 x X X x X

In the figure below what is the value of z 7 5 Z 4 Select one O a 6 O b 5 6 O c 2 9 O d 8 75

2 Find each indicated measure for OM U 36 T a mZs Q O b mTS c mQU d m TMS M R S 102

1 Find each indicated measure for OM D a mEF b m ZE 55 c mZF d mDF 96 M E F

If mAB 38 and mZCED 102 find mCD A C 38 Select one O a O b 102 O c 70 O d 140 E 102 LLI 166 B D

1 A circle is inscribed in a quadrilateral whose four angles have measures 86 78 99 and 97 Find the measures of the four arcs between consecutive points of tangency

Find m ZB if mAB 120 and m ZA 42 A 120 42 Select one O a 60 O b 78 O c 18 O d 156 C B

A circle with center 1 2 passes through 2 2 Which is true Select one O a The radius is 5 O b The equation is x 1 2 y 2 10 O c The diameter is 10 Od The circumference is 25m

Write the standard equation of the circle in the graph ty 2 1 O b O c O d 4 1 Select one O a x 2 2 y 1 2 x 2 2 y 1 4 x 2 2 y 1 2 x 2 y 1 4 X

What is the center of the circle 2x 2y 32 12x 14y Write your answer in simplified rationalized form

8 A glass containing water is in the shape of a circular cylinder with a radius of 3 centimeters The height of the water in the glass is 10 cm What is the volume of the water in the glass SHOW ALL WORK V Bh T h 713 10 262 74 cm 10 Five spherical marbles of equal size are dropped into the glass The water in the glass rises to a height of 11 centimeters What is the increase in the volume of the contents of the glass Be sure to include units of measure in your answer Show all of your work and briefly explain how you found your answer

Write the standard equation of the circle in the graph op Select one O a O b Oc O d the O x 3 2 y 2 9 x 3 2 y 2 18 x 3 y 2 18 x 3 2 y 2 9 60 d

Which of the following statements is false Select one O a Every diameter is a chord b Every chord is a diameter O c Every diameter is part of a secant O d Every chord is part of a secant

OA is inscribed in a quadrilateral What is the perimeter of the quadrilateral 3 mm 7 5 mm A 2 5 mm Select one O a 150 mm O b 25 mm O c 50 mm O d 60 mm 12 mm

Write the standard equation of the circle in the graph Center 4 0 4 5 Select one O a x y 16 O b O c O d y x 4 2 y 25 x 4 2 y 25 x y 25

For problems 8 and 9 complete the square to find the center and radius of the equation below x 4x y 20y 100 0 What are the coordinates of the center of the circle Input answer as x y Answer Check What is the radius of the circle

A low wattage radio station can be heard only within a certain distance from the station On the graph below the circular region represents that part of the city where the station can be heard and the center of the circle represents the location of the station Which equation represents the boundary for the region where the station can be heard 8 4 O Select one O a x 6 y 1 16 O b x 6 2 y 1 16 O c x 6 2 y 1 32

20 SA LA B 45 Tr 45 T3 773 45 3 9K 9 BL 12 lo q SLOW LA WOH2 TL 31 1211 HT 45TT 36 311 Ma 4 A plastic cylinder is exactly large enough to hold 3 tennis balls stacked one above the other The tenni balls are 6 8 cm in diameter Draw a diagram representing this scenario including the dimensions Find t olume of the cylinder 740 9 6 8cm ant Height h 20 4 d 6 8 Volume V Bh r h 5 TT3 4 20 4 740 86

3 5 cm 6 8cm O 5 In construction a nut is used on a bolt or screw for tightening or holding something together Find the volume of the following nut the face of the nut is a square V 5 8 5 8 1 5 V LA 2B 50 46 cm 5 8 cm 1 5 cm TT3 4 20 4 740 86 an2 Trafhit 2 fm volume 3 577 1 5 2 1175 35 74 50 46 35 74

The point 2 5 lies on the circle centered at the origin with radius 9 Select one True False

What is the equation of a circle with center 3 5 that passes though the point 4 1 Select one O a x 4 y 10 226 O b x 4 y 10 74 Oc x 3 2 y 5 226 O d x 3 2 y 5 74

Write the standard equation for a circle center 10 6 r 6 Select one O a x 6 y 10 36 O b x 10 2 y 6 36 O c x 10 y 6 6 O d x 10 2 y 6 6

graphed below 12 11 10 9 8 7 6 5 4 3 4 5 12 11 10 9 8 7 6 y 5 4 3 2 1 1 1 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 6 7 8 9 10 11 12 X

Find the lateral area 13 yd 11 3 yd 13 yd 13 yd 8 8 yd

Find the diameter of OO If your answer is not a whole number round to the nearest tenth 3 4 O Answer

Find the value of the variable If the answer is not a whole number round to the nearest t X 6 Answer 5 10

Many electronic devices use disposable batteries which eventually have to be replaced Assume that for one particular brand and type of battery the distribution of the hours of useful power can be approximated well by a Normal model The mean is 140 hours and the standard deviation is 4 hours The marketing department wants to write a guarantee for battery life What lifespan should they quote so that they can expect 98 of the batteries to meet the guarantee z 00 01 02 5080 0 0 5000 5040 0 1 5398 5438 5478 0 2 0 3 Table entry 0 4 0 5 0 6 0 7 0 8 04 5120 05 06 5160 5199 5239 5517 5557 5596 5636 5793 5832 5871 5910 5948 5987 6179 6217 6255 6293 6331 6368 6554 6591 6628 6664 6700 6736 6915 6950 7019 6985 7054 7088 7257 7291 7324 7357 7389 7422 7580 7611 7642 7673 7704 7734 7764 7794 7881 7910 7939 7967 7995 8023 8051 8078 7454 8212 8238 8264 8289 8315 8340 8186 8461 8438 8531 8665 8686 8749 8869 8888 9049 9066 9207 9222 0245 9257 0 9 8159 1 0 8413 1 1 8643 1 2 8849 1 3 1 4 15 Z 9032 9192 9222 03 8485 8708 8907 9082 9236 9370 8508 8729 8925 9099 9251 9382 07 5279 5675 5714 08 5319 6026 6064 6103 6443 6480 6808 6844 7157 7190 8944 9115 9265 9394 6406 6772 7123 8554 8770 8962 9131 8577 8790 8980 09 5359 5753 7517 7486 7823 8106 8133 8365 8389 8599 8621 8810 8830 8997 9015 9162 9306 9429 9147 9292 9279 9406 9418 6141 6517 6879 7224 7549 7852 9177 9319 9441

Find the value of each variable If the answer is not a whole number round to the nearest tenth 120 Input answer as x y z Answer

Find the value of x 20 Answer 90

In the circle draw each of the following 1 a chord AB that is not a diameter red ink 2 points C and D such that an arc from C to D measures about 120 degree blue ink 3 central angle EOF that measures about 45 degrees green ink angle measures do not need to be perfect but should look to be about that angle measure x Clear Undo Redo

Find the equation for the circle with center 2 3 and passing through 4 1 Which is the correct equation OA x 2 y 3 36 OB x 2 y 3 2 OC x 2 y 3 52 OD x 2 y 3 16

Write an equation of a circle with diameter AB A 2 2 B 14 14 Choose the correct answer below OA x 8 8 7 OC x 2 y 2 14 OE x 8 y 8 72 OG x 8 y 8 2 OB x 8 y 8 2 14 OD x 14 y 14 2 OF x 8 y 8 72 OH x 8 8 72

Complete the sentences below using the dropdown menus for each entry E A H G F The image above shows 2 triangles 1 Name a perpendicular bisector 3 Name an angle bisector R 2 Of the 2 segments LS and LP which shows the distance from point L to a vertex of the triangle C POSSIBLE POINTS 5 71 4 Of the 3 segments HJ HK and HF which shows the distance from point H to a side of the triangle O

What is the center and radius of the circle x 1 y 25 The center of the circle is 1 0 Type an ordered pair The radius of the circle is Simplify your answer

F 95 Find the measures of angle CFE angle DEF there is a Desmos slide in the lesson where you can draw on this same picture as needed degrees 123 degrees D E

2 A triangular prism has a base with dimensions of 9 inches by 4 inches and a height of 12 inches A triangular pyramid has a base with dimensions of 9 inches by 4 inches and a height of 12 inches Determine the which figure has the largest volume