3D Geometry Questions and Answers

Question 3 Find the missing angles in the following two congruent figures B Points 3 74 A 50 C O 74 50 and 56 O 76 52 and 56 O 74 50 and 55 O 74 50 and 124 E F

Question 6 Figure ABCD is rotated clockwise about the origin through 360 Identify the transformed figure y O Points 1 8 7 6 5 4 3 O D 14 A C 5 4 3 0 4 2 3 4 C A B 5 4 3 2 8 7 6 5 4 3 1 D B y 5 4 3 2 W N 0 1 2 3 4 5 6 F1 3 4 y 12 st 5 A No co 6 7 8 4 B 3 2 C x 41 0 1 1 8 4 5 6 7 8 Reset Reset butt after assessme Rese Questio 1 3 5 7 9

Question 6 Which word does not have a rotational symmetry SOS MOW NOON 1 11 III 0 0 O ii Points 3 O iii Gad WOW IV

Find the volume of a pyramid with a square base where the perimeter of the base is 15 2 m and the height of the pyramid is 21 3 m Round your answer to the nearest tenth of a cubic meter

Find the measures of the indicated angles Which of the following is NOT true The figure is not drawn to scale d 3 C OA a 53 OB b 106 C C 73 OD d 37

Find the volume of the sphere shown Give each answer rounded to the nearest cubic unit 5 mm OA 262 mm OB 524 mm OC 314 mm OD 105 mm

Find the volume of the composite space figure to the nearest whole number 5 mm 11 mm Not drawn to scale O A 546 mm OB 174 mm OC 364 mm OD 438 mm3 6 mm

Find the volume of the cylinder 14 yd O 14 yd OA 1 372 4 312 yd OB 2 7448 624 yd Z OC 196 616 yd OD 6862 156 yd

6 Given the volume of the figure determine the measure of the radius Volumo 26 m3

For problems 1 3 refer to the diagram below A 100 2 R N S 12 Answer X 8 4 y Q 80 What is the value of x

Find the center and radius of a circle with equation x 3 y 6 4 Select one O a center 3 6 r 4 O b center 6 3 r 2 O c center 3 6 r 2 O d center 3 6 r 4

Complete this question in your Desmos activity Lesson 5 6 slide 31 PREVIEW D SWYK Lesson 5 6 Question 1 Rubric 3 Next The points A B and C show the location of 3 small towns The towns are putting their resources together to build a school that they will all share The residents want the school to be the same distance away from each town 1 Use a straightedge to draw triangle ABC 2 Find the location of a point D that is the same distance away from each town After completing the question in the Desmos slide write done below 1 point for drawing Triangle ABC 1 point for using correct process to find point D 1 point for correct location of point D you don t have to name it just mark it with a point

Find an equation of the circle having the given center and radius Center 4 7 radius 3 Choose the correct equation OA x 4 y 7 3 O B x 4 y 7 3 OC x 4 y 7 3 OD x 4 y 7 3

Round your answer to the nearest hundredth F C CO B

1 3 What is of the volume of the cone below to the nearest cubic inch 15 m I I I 4m

6 A junior was studying for their SAT and used the formula A r to determine how much soda a cup could hold What was their mistake What would you tell them about finding how much liquid in a cup

1 Find the volume of the figures below and then order them from largest volume to smallest 15 ft 12 11 6 ft ft 12 ft

2 The cone below is filled with ice cream One scoop of ice cream outside the cone has a volume of 17 in What is the combined volume of ice cream inside the cone and the scoop on top to the nearest hundredth 2 in 13 in

6 Examine the parallelogram HIJK below H I 9x 1 K 7x 71 zoom in Determine which of the following values are correct Select three that apply a x 2 b x 4 C m l 35 d m ZH 145 e m j 150 f m 2K 34 6 0 0 0 0 0

3 3 2 The surface area of the rectangular container pictured is 216 square feet What is the value of x 216 10 feet

In the diagram QR ST 144 CU 3x and CV 6x 21 a Find CU 3x b Find the radius of OC 9x S W GF

In the figure below AD 140 and BC 26 What is the measure of ZAED A 140 26 B C E D

2 Sarah has an eBay store She will pay for shipping for parcels that are not more than 25 kg and have a volume of 17 000 cm Sam buys an item from Sarah s store The density of his parcel is 0 002 kg cm3 the height is 25 cm the width is 18 cm and the length is 30 cm You have to calculate the mass of the parcel Does this parcel qualify for free shipping

1 One right circular cone is set inside a larger right circular cone Find the volume of the space between the cones if the diameter of the inside cone is 9 in the diameter of the outside cone is 15 in and the height of both is 8 in Round to the nearest tenth

2 The two figures below are similar ALAL 10 ft 8 ft 15 ft a What is the scale factor of the first figure to the second figure If necessary simplify the ra b What is the ratio of their surface areas c What is the ratio of their volumes

4 Use the formula SA ph 2B to find the surface area of the rectangular prism below Show your work 4 8 ft 2 2 ft 1 9 ft

5 Serena is drawing pictures of cross sections of the right circular cone below Which drawing cannot be a cross section of the cone 1 2 3 4

Question 10 Points 1 Which of the following transformations carry the given regular polygon onto itself O Translation O Reflection O Dilation O None of the choices

3 Determine the surface area of the sphere below with a radius of 5 Express you 5

Question 2 What is the order of rotational symmetry for a regular heptagon seven sided regular figure 07 O 5 Points 1 O6

6 Find the volume of the figure below 9 ft 3 ft 7 6 ft 12 ft 4 ft 3 A 646 88 ft B 466 88 ft C 664 88 ft D 684 48 ft

The measure of the side of a cube is 6 ft The measure of the side of a second cube is 18 ft What is the scale factor of the cubes Select one O a 1 27 O b 1 2 O c 1 3 O d 1 9

A roof is being added to a building at an angle of 20 see the image below Assume that the distance on the roof from the ledge to the center measures 50 feet How much higher off the ground is the center of the roof than the ledge of the roof Round your answer to the nearest thousandth of a foot T O 18 199 feet O 46 985 feet O 53 209 feet 17 101 feet 12 856 feet 0 20

The volumes of two similar solids are 729 m and 125 m The surface area of the larger solid is 324 m What is the surface area of the smaller solid Select one O a 200 m Ob 56 m O c 100 m O d 180 m

14 A cylinder whose radius is 2 inches is removed from the right prism as shown The ends of the prism have the shape of an equilateral triangle whose sides are 8 inches long Find the volume of the remaining solid in cubic inches Dimensions are in inches 8 8 10

2 A box of snack crackers is in the shape of a triangular prism What is the surface area of the box Round your answer to the nearest tenth 5 cm 14 cm 5 cm 4 3 cm 5 cm

Are the two figures similar If so give the scale factor of the first figure to the second figure 10 cm 32 cm A 14 cm 20 cm Are the two figures similar Select the correct choice and fill in any answer boxes in your choice below OA They are similar The scale factor is OB They are not similar Simplify your answer

Find the volume of the square pyramid Round to the nearest tenth if necessary 3 cm 5 cm 3 cm Select one O a 5 cm O b 12 cm O c 4 cm O d 15 cm

The diameter of a planet is about 16 008 mi The diameter of the planet s moon is about 29 of the diameter of the planet What percent of the volume of the planet is the volume of its moon of the volume of its planet The volume of the planet s moon is Round to the nearest whole number as needed

Find the surface area and volume of the figure 12 ft The surface area is 716 3 ft2 Round to the nearest tenth as needed 3 The volume is ft Round to the nearest tenth as needed 10 ft

Find the volume of a sphere with a surface area of 1764 in 3 The volume is in Type an exact answer in terms of it

Find the volume of the triangular prism 7 mm 35 mm 18 mm

The plane region is revolved completely about the y axis to sweep out a solid of revolution Describe the solid Then find its volume in terms of Describe the solid The solid is a cone V 0 Type an exact answer in terms of t 6 4 2 10 8 6 4 2 Ay 2 0 2 4 G O G

What is the volume of the square pyramid V mm Round to the nearest tenth as needed

K Find the volume to the nearest whole number V in Round to the nearest whole number as needed 3 in square base

In a chemistry lab students use a filter paper cone to filter a liquid The diameter of the cone is 12 5 cm and its height is 13 cm How much liquid will the cone hold when it is When it is full the cone holds about Round to the nearest tenth as needed cm of liquid

3 Which 3D figure would this net make

2 Which 3D figure would this net make a Cube b Pyramid c Triangular Prism d Rectangular Prism

1 Which 3D figure would this a Cube b Pyramid c Triangular Prism ular Prism

5 12 23 7 14 AM Question 7 Which overhead view of an office tower appears to display both horizontal and vertical symmetry A B C D B