3D Geometry Questions and Answers

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

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

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

Question 4 Points 2 Find the surface area of a brick with a length of 9 inches a width of 6 inches and a height of 4 inches O 110 square inches O 198 square inches 228 square inches O 270 square inches

Question 3 Points 3 The height and diameter of a cylinder are equal Find the volume of the cylinder if the radius is 5 in 150 in 50m in 250 in 350 in

on Posttest Points 2 The surface area of a cubical box is 121 5 square feet Find the length of the base Question 6 O 3 5 ft O 3 75 ft 4 5 ft O 4 75 ft

Question 2 Points 2 Find the total surface area of the cylinder if its diameter and height are 12 in and 24 in respectively Use 3 14 1 130 4 in O904 32 in O 678 24 in O 226 08 in

14 Use the Triangle Inequality to determine whether it is possible to draw a triangle with sides of the given measures 16 17 20 O Yes O No

5 A ship is being blown by a breeze with a force of 100 N on a bearing of 280 as on a bearing of 170 A tugboat holds it in place Find the size and bearing of the shown in the diagram It is pulled by a rope attached to the shore with force 50 N force F applied by the tugboat 100 N 80 north 0 170 50N

14 A particle has three horizontal forces acting on it as shown in the diagram Show that cos a 14 13 cos B and find an expression for sin a Use 15 cos a sin 1 to get an equation in B Hence find a and B 14N a 15 N

Find the volume of the composite figure Round to the nearest whole number Volum 8 cm 16 cm 14 cm pal

15 x 3 Answer Three units behind the yz plane 16 z 5 17 y 0 Answer To the left of the xz plane

Finding the Equation of a Sphere In Exercises 43 44 45 and 46 complete the square to wri the equation of the sphere in standard form Find the center and radius 43 x y 2 2x 6y 8z 1 0 Answer x 1 y 3 z 4 25 Center 1 3 4 Radius 5

Question 14 Quelle est la mesure de la ligne orange qui se trouve dans ce prisme base carr e R ponse 12 m 5 m

Ekshitha leads an organization where the culture is family like and emphasizes mentoring nurturing and doing things together What type of culture is Ekshitha promoting Adhocracy Clan Hierarchy Market

11 Find the circumference of the circle The units are in feet use 3 14 as pi and round your answer to two decimal places feet

5 Find the circumference of the circle whose diameter is 14 meters Exact Answer C TM Approximate Answer Round to 2 decimal places C m

Question 6 Points 2 Find the area of a sector of a circle if the radius is 25 mm and the central angle is 300 Use 3 14 1635 42 mm O 1423 69 mm O 1267 45 mm O 1127 45 mm

Problem 4 20 Points Use one of the golden triangles to prove that cos 36 is the golden ratio where o

Question 6 Find the equation of a circle whose center is at 1 2 and passes through the point 4 1 O x y 4x 2y 13 0 O x y 2x 4y 13 0 O x y 2x 4y 23 0 x y 4x 2y 23 0

2 Describe in words and a simple sketch the solid given by the following inequalitie a 0 p 2 0 6

A ladder leaning against a building makes an angle of 78 degrees with the ground TF foot of the ladder is 5 feet from the building How long is the ladder

13 Given mAB 114 and mDC 38 Find m 1 point A B D C

6 Given right ADEF with DE 6 2 and m FEK 135 Find EF and DF D 1 point 6 2 E

In the figure for Exercises 7 to 16 O is the center of the circle See Theorem 6 3 5 11 Given Find AE CB 6 EC 3 AD 8 D A E Exercises 7 16 3 B C

3 Given 2 Find R T Circle O with diameter RS tangent SW chor TS and mRT 26 a m WSR b m RST c m WST W S

13 Given Find OO with AB AC and 72 m BOC a mBC b mAB c m A d m ABC e m ABO B ST A

ma circle of radius 7 feet what angle would subtend an arc of length 2 feet degrees

What is the entropy change of 1 mol of XO3 for the reaction XO2 g 1 202 g XO3 g XO2 S 247 11 O2 S 205 0 XO3 S 247 76 Give answer to two decimal places Do not include units in your answer Your Answer

Use the standard reaction energies given below to determine AG rxn for the following reaction 2XO2 g 2XO g O2 g From the standard reaction energy of X2 g O2 2XO g DG 163 77 kJxmol 1 X2 g 2O2 g 2XO2 g DG 190 17 kJxmol 1 Give answer in KJ mol Give answer to two decimal places Do not include units in answer Your Answer

Calculate AGrxn at 298 K under the conditions shown below for the following reaction Fe2O3 s 3 CO g 2 Fe s 3 CO2 g AG 34 1 kJ 1 P CO 0 7 atm P CO2 1 7 atm Please report the answer with one decimal place Your Answer

Question 4 A golf ball is 9 feet from the edge of the stadium and 15 feet from a point of tangency on the stadium as shown in the figure What is the radius of the stadium O 9 ft O 8 ft Points 3 O 7 ft 9 ft A 15 ft B F a Qu 3 5 7 9

Question 10 Find the length of AB in the triangle CAB Round off your answer to the nearest tenths place C 72 56 3 3 4 8 O 5 2 O 6 9 Points 2 5 B Rese Reset enabl this as R Ques 1 3 5 7 9

The measure of the two angles A and C are given in the triangle Find the length of the side opposite to angle C Round off the answer to the nearest tenths place C 69 62 O 6 9 8 5 O 9 5 6 O 10 2 C B

Question 1 Points 2 Find the measure of the side AB in the figure using the given information a 3 b 5 C 60 C A O 3 5 O4 4 4 O 4 6 b C a B Rese Reset enabl this a R Ques 1 3 5 7 9

Question 8 Points 2 Which of the following is true about the circle C1 to C2 Y 7 2 C1 2 N 2 4 C2 0 2 X O Circle C1 is translated 3 units right and 4 units up O Circle C1 is translated 4 units right and 3 units up O Circle C2 is translated 3 units right and 4 units up

Question 7 Points 3 Find the translation rule and the scale factor of the dilation by transforming the circle C to C AY 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 2 3 5 6 7 8 9 10 C 1 2 3 4 5 6 7 8 9 10 Translation 11 units to the right and 8 units up Scale factor enlargement ratio 4 Translation 7 units to the left and 11 units down Scale factor reduction ratio 1 3 Translation 11 units to the right and 7 units up Scale factor enlargement ratio 3 Rese Reset after asses R Ques 1 3 5 7 9

3 Rewrite the following statement as a conditional statement Jim didn t study for his test so he failed the class O If Jim did not fail his class then he studied for his test If Jim fails his class then he didn t study for his test If Jim studies for his test then he will not fail the class Olf Jim doesn t study for his test then he will fail the class

Find the measure of the side AB Round your answer to the nearest whole number A 12 45 C 20 22 23 a 30 B

If the image is smaller than the original figure then the dilation is a ar congruent O enlargement reduction rigid transformation