3D Geometry Questions and Answers

2 The Great Pyramid outside Cairo Egypt has a square base measuring 756 feet on a side and a height of 480 feet a 3 pts What is the volume of the Great Pyramid in cubic yards Work 2 pts Replace these words with a cropped picture of your work for question 2a only Answer 0 5 pt Reasoning Explanation 0 5 pt X b 2 pts The stones used to build the Great Pyramid were limestone blocks with an average volume of 1 5 cubic yards Assuming a solid pyramid how many of these blocks were needed to construct the Great Pyramid

A rectangular box meets the following criteria All lengths are measured in feet The length is twice as long as the width The height is 1 foot shorter than the length The volume of the box is 147 ft Find the dimensions of the box width W length L height H feet feet feet

Activity In this activity you will use the GeoGebra geometry tool to explore the side side side criterion for triangle congruence If you need help watch these short videos about using GeoGebra to measure and create points lines and angles C Part A Create a triangle using the vertices A 4 3 B S 2 and C 2 6 Measure the lengths of all three sides on the triangle using the distance tool and record them in the table BIY X X 14pt Bwww Side Length AB BC AC Space used includes formatting 560 15000 EFFE Part B Keep the triangle that you created in part A You will now copy the triangle to a different location on the grid using three of its sides Submit In a different place on the grid draw a new line segment that is parallel to and has the same length as AB Label this segment DD Next copy AC and BC A reliable way to do this is to draw a circle centered on each endpoint of your new line segment Make the radius of each circle equal to each of the lengths of the two remaining line segments on the original triangle One of the intersection points of the two circles marks the third vertex of your new triangle Place a point on the intersection and label the point F Finish copying the triangle by drawing a polygon through the three points that you ve established BIY X X 15px You should now have two triangles on the grid What do you notice about the two triangles in terms of their size and shape V AVA EF a 8

Find all of the angles of rotation including 360 for a regular decagon a ten sided polygon KA T U sans serif www

ABC and ADEF have congruent corresponding angles and satisfy the AAA correspondence ABC and ADEF are always congruent may or may not be congruent AAA correspondence Reset Next a criterion for congruency of any two t

1 1 point Match each set of level curves with the appropriate graph of function Briefly explain your choices 1 2 3 OXO a b C

A triangle has side lengths BC 9 AB 7 and AC 13 Which angle in the triangle has the greatest measure ZA answer Cannot be determined ZB

How does the figure verify the triangle inequality theorem 4k 11 O by showing that the sides with lengths of 7 and 4 can form many possible triangles by showing that the sides with lengths of 7 and 4 can meet to form a third vertex by showing that the sides with lengths of 7 and 4 will never meet by showing that the sides with lengths of 7 and 4 will only meet when they lie on the third side O O O

Y sec x 1 y tan x y N y 3x 2 1 YOOOL 3 2 2x R Y 4 3 x 2 7 2 3A 4 JUDUL 3 2 R 2 A 3x 2 1 2 91 J2 2 2x X 2x X No the functions are equivalent except when tan x nit 2 JU U VL 3 2 3A 3A nit No the functions are equivalent except when sec x 1 7 YANG 3 2A 2 27 R 3 A 2 y JUUL y y H Use the graphs to determine whether the expressions are equivalent Verify the results algebraically O Yes the expressions are equivalent 2 1 2 3x 2 27 2x

Date Name Read and respond to each question carefully Show work for full points Test is scheduled for Thursday October 5th 2023 tentative 1 Find the length of XY Explain how you found your answer 6 12 2 Point Mis between points L and Non LN LN 6x LM 4x 8 and MN 27 Use the information 6x Use the diagram 3 Give another name for line S 4 Name three points that are coplanar 5 Name three points that are collinear 6 Give another name for plane K 4 2 4x 8 2 2 M 27 7 Plot the points in a coordinate plane Then determine whether AB and CD are congruent 3 2 R Period P 8 The endpoints of CD are C 1 6 and D 7 5 Find the coordinates of the midpoint M 9 The midpoint of RS is M 1 2 One endpoint is R 6 6 Find the coordinates of endpoint S

point Each graph below is the graph of a system of three linear equations in three unknowns of the form Az b Determine whether each system has a solution and if it does the number of free variables A choose D choose 8 choose choose choose F choose

11 In the figure at right what is mPQ mPRQ La bas To Tadil TOW sigasi Poel sit com c 12 Use your compass and protractor to make an arc with measure 65 Now make an arcuri 110 with measure 215 Label each arc with its measure O 13 Name two places or objects where concentric circles appear Bring an example of a set of concentric circles to class tomorrow You might look in a magazine for a photo or make a copy of a photo from a book but not this book 14 Sketch two circles that appear to be concentric Then use your compass to construct a pair of concentric circles R e

Respond to each of the following a Explain why Figure A is not the image of Figure B after a rotation about point P B B P A b Explain why Figure B is not the image of Figure A after a reflection across line l A

left 2 Select all the sequences of transformations that could map Figure X onto N Y O X A a single translation B a single reflection C a single rotation D a reflection then a different reflection E a translation then a reflection X

Use the given E 1 F H Statement G J K Given EF JK FG HJ Prove EG HK Reason Send To Proof Send To Proof Send To Proof

1 In the photos below identify the physical models that represent a circle a radius a chord a tangent and an arc of a circle ction tools for Exercises 12 17 18 22 23

11 Triangle EFD was made by reflecting triangle ABC across 12 B 2 24 71 6 2 83 63 4 45 3 00 A B C Name pairs of corresponding angles from triangles ABC and EFD rocponding sides from triangles ABC and EFD then translating E D 3 00 63 4 45 2 24 71 6 2 83 F

E The diagram shows a vertical pole PQ which is supported by two wires fixed to the horizontal ground at A and B Find a b BQ 40 m PBQ 36 BAQ 70 ABQ 30 the height of the pole PQ the distance between A and B 70 A 360 og 300 B

17 An acute angle is an angle whose measure is less than 90 18 If two lines intersect to form a right angle then the lines are perpendicular 19 A diagonal is a line segment that connects any two vertices of a polygon

3 3 If two secants P and PC of a circle meet the circle at A B and C D respectively then PA x PB PC x PD 6 Ac

21 3 900

4 The height of a building is 72 m Find the angle of elevation from a point on ground level that is 55 m away from the base of the building 5 From a boat 160 m out at sea the angle of elevation to the coast is 18 The angle of elevation to the top of a lighthouse on the coast is 22 a Draw a diagram representing the situation b Find the height of the lighthouse

Determine the length of each arc with radius r and central angle a given below Give your answer correct to 2 dp a r 5 cm 70 b r 4 cm 45 c r 10 5 cm a 130 The London Eye is a giant Ferris wheel in London It is the tallest Ferris wheel in Europe with a diameter of 120 m The passenger capsules are attached to the circumference of the wheel and the wheel rotates at 26 cm per second a the length that a passenger capsule would travel if the wheel makes a rotation of 200 b the time in minutes that it would take for a passenger capsule to make a rotation of 200 t the time to the nearest whole minute that it would take for a passenger capsule to make a full revolution

3 With 72 million bicycles correct to the nearest million Japan is at the top of the list of countries with most bicycles per person On average Japanese people travel about 2 km by bicycle correct to the nearest km each day Calculate the upper bound for the total distance travelled by all the bicycles in Japan per day 4 To determine whether a business is making enough profit the following formula is used P C S C S where P is relative profit S is sales and C is costs If a company has 340 000 worth of sales and 230000 of costs correct to 2 significant figures calculate the maximum and minimum relative profit to the ate

20 Name the following in the diagram below Intersection of 2 Segments Intersection of 2 planes 1 L sc ban 21 P nouammolni nsvig sdt In diw og does am Two skew segments d What is a Vertex SACS 08 CA POR M R TA OA SOTH STAD OR Om Tr

K For Exercises 16 and 17 mark each figure with all the given information 16 mLADB 90 AD BD LDAB LDBA A B D C 17 m RPQ 90 QR TZ RT QZ LQ LT R 47 P T 3673879 xemay

your answer to the nea 44 3 X 11 11

Find the reference angle for 320 0 010 X B JU

a Line k is not parallel to AB Line k does not intersect AB AB is reflected over line k to produce A B Part A Alex says The distance from point A to A equals the distance from point B to B Is Alex s statement correct or incorrect Justify or explain your answer Enter your answer and your justification or explanation in the box provided BiU X x C

Determine the volume of a right trapezoidal cylinder whose bases are B 16 m and b 9 m height is h 3 m and length is 1 17 m b B 1 1

2 12 points i and u are vectors in 3D space satisyfing 5 6 7 15 a Find the angle between u and b If u and 7 lie in the plane x y z 0 find a vector that is either ux v or v x u

The function r t traces a circle Determine the radius center and plane containing the circle r t 4i 12 cos t j 12 sin t k Plane x 4 Circle s Center Radius 9

Callie is sending her nephew a soccer ball for his birthday She packs the ball in a cubic box that has the same side length as the diameter of the ball She needs to determine how much space needs to be filled with packing material Use 3 14 or the button on your calculator Round all results to the nearest hundredth box If the sides of the box are 24 cm soccer ball a What is the volume of the box 13 824 b What is the volume of the ball of cm cm c What is the remaining volume of the box that needs to be filled with packing material Enter an integer or decimal number imo

Sketch the triangle with vertices O P 6 4 0 and Q 0 6 4 and compute its area using cross products Area

2 3 4 5 6 7 8 9 The diagonal dashed line represents a new line of reflection Position the red tetronimo such that its reflection about this line of reflection fits the gap shown Enter as x something y something Reflect

Find sin 2x cos 2x and tan 2x if cosx sin 2x cos2x 0 0 C 1 5 and x terminates in quadrant IV 2 16 X

The connector rod from the piston to the crankshaft in a certain 1 0 L engine is 5 9 in The radus of the crank circle is 2 8 m If the angle made by the connector rod with the horizontal at the wrist pin P is 24 how far is the wrist pin from the center C of the crankshaft Round to the nearest tenth of an inch 2 8 in 59 m 24 The distance from the wrist pin to the center of the crankshaft is approximately in or 1 X

Many formulas are used in mathematic courses Please match the volume formula to its solid A r h 3 B r h C area of base x height D area of base height 3 4 E A B C D Choose Choose Cylinder Cone Pyramid Sphere

actory makes aquariums Each aquarium is in the shape of a triangular prism as shown below If the factory made aquariums that require a total of 1152 ft water how many aquariums did the factory make 4 ft 2 ft 3 ft aquariums X

A company makes wax candles in the shape of a cylinder Each candle has a diameter of 8 inches and a height of 3 inches If the company used 5727 36 in of wax how many candles did it make Use 3 14 for and do not round your answer

14 pts Hyperbola with perpendicular asymptotes are called equilateral or rectangular hy perbola Lines are perpendicular when the product of their slopes is equal to 1 Is this an equilateral hyperbola For full credit you must show all your work and provide clear rationale for your answer 6x 6y 12x 48y 6 0

Question 48 What three dimensional figure models a hockey ball O Cone Points 1 O Cylinder O Sphere O Cube

Points 1 Which of the following formulas is used to find the volume of a cylinder with a radius of r units and a height of h units O Trh cubic units O 2 r h cubic units Trh cubic units r h cubic units

7 Name all angles which are congruent d 8 O a and d b and c e and h g and f a and e b and g c and f d and h O a and c b and d e and f g and h a and b c and d e and g f and h

2 Find the volume of the box whose length width and height are given respectively 15 mm 2 mm and 5 mm V mm 3

1 Find the volume of the box below V 8 in in 3 3 in 3in

QuestionT Identify the three dimensional figures A A and D B and D A and C B and C

5 For the right circular cylinder suppose that r Sin and h 6 in Find the exact and approxe a lateral area b total area c volume Exercises 3 6 6 Suppose that r 12 cm and h 15 cm in the right circular cylinder Find the exact and approximate a lateral area b total area c volume h

The tin can shown at the right has the indicated dimensions Estimate the number of square inches of tin required for its construction HINT Include the lid and the base in the result 1 1 2 in 4

4 Find the area of an a a perimeter of 24 6 cm b a radius of length 4 in equiangular triangle with