3D Geometry Questions and Answers

A group G of six matrices is generated by A 11 and B 3 under matri multiplication modulo 2 List the six matrices in G if G is isomorphic to S3

0 r 3 2 plane co TU y 4 2 sting of points whose polar coordinates satisfy the given conditions 2 2 X 4 2 y 4 4 4 2 y 2

Simplify sec 900 8 cot 90 0 O csc tan 0 O sec 0 cot 0 O cos 0 sin 0 O sin 0 cos 0

8 perpendicular to the line y 2x 3

20 Find the number of sides for a regular polygon whose exterior angles each measure a 45 b 9 STO

8 Find the radius The units are in feet feet 16

4 If AB is 30 feet find the diameter of the circle feet 5 Explain how you got your answer A What properties did you use B What formula did you use

In Exercises 1 to 6 and m are cut by transversal v On the basis of the information given determine whether must be parallel to m 1 m1 107 and m25 107 2 m2 65 and m 7 65 3 m 1 106 and m 7 76 4 m 1 106 and m24 106 m 1 2 3 4 5 6 7 8

What is the equation of the circle with center 0 0 that passes through the point 8 3 Select one a x y 73 b x y 55 c x 8 2 y 3 55 d x 3 y 3 73 Check

The equation of a sphere is similar to the equation of a circle The equation of a sphere with center h j k and radius r is x h y j z k r M 2 3 3 is the center of a sphere passing through T 0 4 2 What is the radius of the sphere What is the equation of the sphere The radius of the sphere is Type exact answers using radicals as needed

2 If there were no understood restriction to lines in a plane in Theorem 1 4 3 the theorem would be false Explain why the following statement is false In space there is exactly one line perpendicular to a given line at any point on the line

In Exercises 55 and 56 P is a true statement while Q and R are false statements Classify each of the following statements as true or false 55 a P and Q or R b P or Q and R

Which type of path straight curved circular or scattered is determined by a a roller coaster b a pencil c d darts thrown at a dartboard a carousel

17 Use the angle symbol 2 and three letters to name the angle formed by the two rays CD and CE rays not shown

12 Given DE bisects ZCDA and 23 21 Prove DE AB Proof 1 2 23 22 3 4 Statements 3 points 1 Given 2 E A 3 D 2 Reasons 3 Transitive Property of Congruence B 4 If two lines are cut by a transversal so that two alternate interior angles are congruent then these lines are parallel

Describe the cross section formed in the diagram below Select one a equilateral triangle b trapezoid c isosceles triangle Od cone A food company makes regular and tall soup cans The area of the base of both cans is 30 cm The volu of the regular can is 270 cm The tall can is 2 cm taller What is the volume of the tall soup can Select one a 300 cm b 540 cm Time left 1 c 330 cm d 295 cm

The volumes of two similar solids are 729 m and 125 m3 The surface area of the larger solid is 324 m What is the surface area of the smaller solid Select one a 56 m b 100 m c 180 m d 200 m Check A shipping box holds 350 golf balls A larger shipping box has dimensions triple the size of the other box How many golf balls does the larger box hold Select one a 3150 b 1050 c 9450 d 2800

Square pyramids A and B are similar In pyramid A each base edge is 8 cm In pyramid B each base edge is 2 cm and the volume is 4 cm a Find the volume of pyramid A b Find the ratio of the surface area of A to the surface area of B c Find the surface area of each pyramid a The volume of pyramid A is Simplify your answer cm

The volume of a spherical balloon with radius 2 9 cm is about 102 cm Estimate the volume of a similar balloon with radius 8 7 cm The larger balloon has a volume of about cm

Solve the inequality h 2 6h 10 Give your answer in interval notation Enter DNE if there is no solution

Find the volume of the sphere to the nearest cubic centimeter Select one a 205 cm b 359 cm c 11 494 cm Od 1 437 cm Check 14 cm elect one he volume of a sphere is 5000 m What is the surface area of the sphere to the nearest square meter Sucato a 1 517 m b 195 m c 3 033 m d 62 832 m

oints A spherical balloon has a 20 in diameter when it is fully inflated Half of the air is let out of the balloon Assume that the balloon remains a sphere a Find the volume of the fully inflated balloon b Find the volume of the half inflated balloon c What is the diameter of the half inflated balloon a The volume of the fully inflated balloon is Simplify your answer Type an exact answer using pi as needed Use integers or fractions for any numbers in the expression

lue of x in the figure 1500 15 alue of x in the figure 3 81 4

A pyramid shaped building is 843 ft tall with a square base that is 134 ft on each side What is the volume of the pyramid v 1 Round to the nearest tenth as needed

K Find the volume of a square pyramid with a height of 10 m and base edges of 6 m 3 V m Round to the nearest tenth as needed

Find the volume of the cylinder in terms of it 8 5 m 17m Select one a 59 5 m b 505 8 m c 373 8 m d 416 5 m Check Find the volume of the cylinder to the nearest tenth 2 mm 10 mm Eelect one O a 502 7 mm Ob 62 8 mm c 125 7 mm 000 mm

Find the volume of the composite space figure to the right to the nearest whole number The volume of the figure is cm Simplify your answer its 0 of 1 10 cm 3 cm Sa 4 cm 7 C 13

The plane region is revolved completely about the x axis to sweep out a solid of revolution Describe the solid and find its volume in terms of t Describe the solid Choose the correct answer below OA The solid is a cylinder with a radius of 4 OB The solid is a rectangular prism with a base length of 3 OC The solid is a rectangular prism with a base length of 4 OD The solid is a cylinder with a radius of 3 2 2 2 4

Find the volume of the cylinder in terms of and to the nearest tenth The volume in terms of is V in Type an exact answer in terms of 1 in 2 in

e lateral area of the cone in terms of T one 80T 96 36 60TT e surface area of the cone in terms of 10 6 AT one 72 80T

3 in J Answer Check 10 in 7m 3 in Use formulas to find the lateral area and surface area of the prism Round your answer to the nearest whole number Select one 7m 7m the nearest whole number a 196 m 343 m b 294 m 343 m c 196 m 294 m

Suppose that a cylinder has a radius of r units and a height of 2r units The lateral area of the cylinder is 64m square units What is the value of r Select one a 8 units b 2 units C 4 units d 16 units Check What is the surface area of the cylinder Round your answer to the nearest square unit Select one a 226 square units b 616 square units c 302 square units d 1809 square units

Find the surface area of the cylinder in terms of 9 cm Select one Not drawn to scale a 211 5 cm b 504 cm c 382 5 cm d 333 cm 19 cm

problems 7 and 8 use the figure below ify Euler s Formula for the polyhedron ect one a b C d 2 4 4 2 6 6 4 3 5 2 7 7 4 4 6 2 8 8 3 3 4 2 6 6

There are five regular polyhedrons They are called regular because all their faces are congruent regular polygons and the same number of faces meet at each vertex They are also called Platonic solids after the Greek philosopher Plato A B Tetrahedron Match each net below with a Platonic solid B D Choose Choose C Choose Choose Hexahedron Octahedron Dodecahedron D C A Icosahedron

scribe the solid of revolution you get by revolving the region below about line L ect one a The solid of revolution is a cone b The solid of revolution is a circle c The solid of revolution is a sphere Od The solid of revolution is a cylinder Check escribe the solid of revolution you get by revolving the region below about line L ect one a The solid of revolution is a sphere b The solid of revolution is a pyramid c The solid of revolution is a cylinder

34 If the measure of the central angle theta is 62 degrees what is the measure of arc AB i 31 62 124 360 25 Whisk

22 21 The inside of an ice cream cone is filled with ice cream and has a radius 6 cm and a height of 12 cm Assuming that a half scoop of ice cream is in the shape of a hemisphere and that it fits perfectly on top of the cone same radius find the total volume of ice cream Round your answer to the nearest tenth A 881 0 cm B 904 8 cm C 1357 2 cm D 1809 6 cm O A OB O D 23 12 6 cm

17 Find the volume of the pyramid Find the Vom of the square pyramid with a slant height of 13 cm base lengths of 10 cm and a height of 12cm A 340 sq cm B 360 sq cm C 400 sq cm D 1200 sq cm O A OB E

13 Find the volume of the cylinder 7 mm 0 8 mm O O 112 square mm O 351 68 square mm O 1 230 88 square mm 56 square mm

9 12 The surface area of a basketball is 277 in What is the radius of the basketball to the nearest tenth of an inch O A OB O C O D A 4 7 in B 9 4 in C 22 0 in D 88 2 in 10 What in the lin

Verify Euler s Formula for the polyhedron to the right Then draw a net for the figure and verify Euler s Formula for the two dimensional figure Verify Euler s Formula for the polyhedron Choose the correct answer below OA 6 6 10 2 12 12 OB 7 5 10 2 12 12 O c 8 5 11 2 13 13 OD 8 6 12 2 14 14

How many vertices faces and edges are in the polyhedron to the right List them How many vertices in the polyhedron List them A There are eight vertices Q B C D M V W and H B There are eight vertices H W V M I D C and B OC There are seven vertices W Q B H C M and V D There are seven vertices M Q D C W H and B G Q M B 1 1 1

Find the volume of the solid below 5 cm 4 cm 3 cm 7 cm 4 cm 6 cm 3 cm

R W 0 1 Z 1 3 y X 4 0 Y 3 2 What is the perimeter of parallelogram WX O 5 17 units O 2 5 2 17 units O 16 units O 22 units

What is the surface area of this complex figure O 5 492 8 cm O 6 597 3 cm O 7 701 8 cm O 8 806 2 cm Z 37 5 cm 27 875 cm

se the fact that matrices A and B are row equivalent 1 21 0 0 2 5 1 1 0 3 7 2 2 2 8 18 6 2 8 10 30 4 1 0 A B WN 01 00 00 2 0 1 2 000 a Find the rank and nullity of A rank nullity b Find a basis for the nullspace of A c Find a basis for the row space of A

The figure below shows a block of butter Which shape does the intersection of the vertical plane with the block of butter like O Circle O Rectangle O Triangle Square

Use rigid motions to prove that figure ABC is congruent to figure EFG B C F G

In the diagram below draw the two limiting parallel lines to the given line I and a point P on the Poincare model of hyperbolic geometry Indicate the two angles of parallelism for I and P