3D Geometry Questions and Answers

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 silo is in the shape of a cone The silo is 8 meters tall and its base has a diameter of 3 meters Soybeans cost 414 per cubic meter How much will it cost to fill the silo with soybeans Use 3 14 for it and do not round your answer

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

etermine the equation of the parabola whose graph is given below Write your answer in General Form Provide your answer below 7 6 5 4 3 2 777 3 5 6 7

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

13 Assume that the number of sides in the base of a pyramid is n Generalize the results found in earlier exercises by answering each of the following questions a What is the number of vertices b What is the number of lateral edges c What is the number of base edges d What is the total number of edges e What is the number of lateral faces f What is the total number of faces Note Lateral faces and base faces

5 In the solid shown base ABCD is a square a Is the solid a prism or a pyramid b Name the vertex apex of the pyramid c Name the lateral edges d Name the lateral faces e Is the solid a regular solid E A B Exercises 5 7 9 11 C M S V N R P Exercises 6 8 10 12

Note Exercises preceded by an asterisk are of a more challenging nature In Exercises 1 to 4 name the solid that is shown Answers are based on Sections 9 1 and 9 2 1 a b

a Base Exercises 14 15 5 In the regular pentagonal prism shown above suppose that each base edge measures 9 2 cm and that the apothem of the base measures 6 3 cm The altitude of the prism measures 14 6 cm a Find the lateral area of the prism b Find the total area of the prism

Note Exercises preceded by an asterisk are of a more challenging nat 1 Consider the solid shown a Does it appear to be a prism b Is it right or oblique c What type of base s does the solid have d Name the type of solid e What type of figure is each lateral face Exercises 1 3 5 7 9

17 For the right triangular prism found in Exercises 16 17 Exercise 16 suppose that the sides of the triangular base measure 3 ft 4 ft and 5 ft The altitude is 6 ft in length a Find the lateral area of the prism b Find the total area of the prism c Find the volume of the prism

9 Find the exact area of the sector Radius of the circle r 12 cm and m AOB 135 A 12 0135 2 points B

8 Find the area of the following figure The units are in feet 12 14 49

Question 7 A shopping mall is decorated for the holidays with spherical balls The balls are of different sizes Which of the following radii fits a ball with a volume of 288 mm 4 mm O 5mm O 6mm Points 2 O 7mm

Question 5 Find the radius of the ball if it has a surface area of 60 square inches O 30 in O 15 in O 30 in Points 2 O 15 in

Find the volume of the sphere whose radius is 10 cm Use 3 14 1 188 cm O 4 282 cm O4 187 cm O 3 128 cm

Question 2 If 1 gallon of paint covers 400 square feet about how many gallons of paint are needed to paint the exterior of a spherical tank of a diameter 30 feet Use 3 14 6 065 O 7 065 08 065 Points 3 8 065

Question 1 Points 2 Find the surface area of a sphere with a radius of 22 cm 6 084 57 cm O 1 024 57 cm O2 585 5 cm O245 67 cm

Question 5 A box has a volume of 336 cubic inches What is the length of the box if the width and height are 7 inches and 6 inches respectively O 5 in O 6 in O 7 in Points 1 O 8 in

Question 9 Points 2 If a cylindrical water bottle has a radius of 4 cm and a height of 12 cm how many cubic centimeters of water will it hold 190 cubic centimeters O 182 cubic centimeters O 192 cubic centimeters 172 cubic centimeters