3D Geometry Questions and Answers

1 Calculate the surface area of a rectangular pris that is 3in by 5in by 2in

4 Calculate the surface area of a cylinder with a radius of 3m and a height of 12m Leave your answer in terms of WA

3 Determine whether you would need to add or subtract to find the volume of the complex figures below a ADD SUBTRACT What two shapes would you find the volume of b 12 in ADD 13 in SUBTRACT What two shapes would you find the volume of

1 Determine the surface area of a cylinder with a diameter of 10 in and a height of 4 in Round to the nearest tenth Draw the figure first

he regular octagon has a perimeter of 122 4 cm 20 cm Y W Which statements about the octagon are true Select two options The length of segment YZ is 15 3 cm O The measure of the angle formed by the radius and the apothem is 30 O The length of segment XY can be found by solving for a in 20 7 65 a O The length of segment WZ is 20 cm The measure of the central angle ZZXW is 45

A regular pentagon is shown 9 4 cm 8 cm What is the length of the apothem rounded to the nearest tenth 2 9 cm 3 3 cm 4 9 cm 6 5 cm

The pentagon below has an area of 8 3 square centimeters 2 2 cm What is the approximate length of the apothem O 0 4 cm O 0 8 cm O 1 5 cm O 1 9 cm

A 101 1 10 101 101 110 110 b 2 2 4 12 5 2 SOXXB The general least squares solutions of Ax b for the given matrix A and vector b are all vectors of the form x Simplify your answers x with x

4 a Draw the area 9x y 9z 18x 4y 18z 32 0 b In a spherical coordinate system draw the area p sin2 cos 20 2 cos

4 Consider the matrix equation Ax b where a b A 1 1 1 where a b 0 a When is A strictly diagonally dominant and what does this tell us about the Gaus Seidel method for Ax b 1 marks b Find the iteration matrix for the Gauss Seidel method applied to Ax b 5 marks c Using your previous answers for what values of a and b does the Gauss Seidel metho 4 marks converge

e If 02 1 rad then what are your xy coordinates after 7 seconds Round your answers to three decimal places x y Draw an accurate picture of the situation start end end start start end start end X

8 0 625 10 0 938 3 0 25 Write a rational function that goes through the dashes on the graph When you finish press Graph and submit response E Graph and submit response

The table shows the lengths of cables needed to connect computers to create a network Find the minimum length of cable using the greedy and edge picking algorithm AB C D E C A 10 22 9 15 8 B C 10 22 12 12 14 16 5 14 9 16 D E 9 15 14 16 14 9 7 7 15 13 F 8 5 16 15 13

3 Line 2 x 2 1 y 1 3A z 5 1 x 7 11 z and Located in a plane The B plane passes through the points A 2 1 0 B 1 0 3 and C 3 1 1 Determine the point distance P 2 4 1 to the intersection of the a and planes 3

3 Line 2 x 2 1 y 1 3A z 5 1 3 x 7 11 z and Located in a plane The B plane passes through the points A 2 1 0 B 1 0 3 and C 3 1 1 Determine the point distance P 2 4 1 to the intersection of the a and planes

3 Line 2 y 7 3 x 3 11 z x 2 y 1 32 z 5 1 and Located in a plane The plane passes through the points A 2 1 0 B 1 0 3 and C 3 1 1 Determine the point distance P 2 4 1 to the intersection of the a and planes

6 Find the surface area of the solid 5 8 10

Find the volume of the composite figure 5 in The volume of the composite figure is 2 in 8 in cubic inches 2 in 5 in

If the m FMN x 20 m FML x and m LMN 150 Find the m FMN N F M L

Find the volume of the rectangular prism 6cm 3 c 9 cm

below Complete both transformations Then enter the final coordinates of the figure A 2 4 C 3 1 1 3 2 2 Dilate K 4 B A 5 2 B C

3 Find the arclength of the highlighted section 288 9 5 ft

24 Surface Area Find the surface area of the sphere O113in O452in radius 4 in

C Determine the region in the space whose coordinates satisfy the inequalities x y z 4 x zs2 0sys4 0 x Osz 3 44

The figures below are similar 3 ft V 216 ft 5 ft V 1 2 V What is the volume of the larger rectangular pyramid cubic feet

dimensional figure about the x axis Select one 1 5 432 1 5 4 3 2 11 1 2 3 4 5 2 3 4 45 5 a sphere with radius 2 a sphere with radius 4 y a hemisphere with radius 2 a hemisphere with radius 4 X

The figure shows angle LMN La No M S What is the name of the three dimensional shape formed if points M and N remain fixed while line segment LM is rotated around line segment MN

25 Given QRL ST QS RT and the exterior angle P is 27 What is the measure of the missing arcs in the diagram at right mQT m OS m TSR m SR

3 find the volume 1 2 in plume surface area of 3D shapes v bhl 6 in 3 in V 12in 7 in 3 5 2 in V v 1 2 2 v G 2 U12 V 1 Y 3 m 3 5 6 V 3 14 12 25 6 2 4 2 2 in 20 2 in 2 2 in v bhlog 2 v 7 7 8 392 196 49 8 9 9 in 7 in 4 in u Z V 196in v bhl V 7 38 2 8 in

Find the surface area of the square pyramid 9m O 189 m O 486 m O 405 m O 297 m 9 m

Find the surface area of the rectangular pyramid 9 2 t 118 O 230 1 ft O 187 2 ft O 273 7ft O 120 7ft 10 5

3 Given g x a Determine the amplitude 4sin c Write the equation of the midline X 2 d Identify 5 key points for one period g x e Sketch a graph of g x for two full periods V 10 pts b Find the period

what is the product of x and y y C X E ZO x 20 C

P M Z T N B W ADI T W E Part A If you choose two blocks at the same time what is the probability that both blocks will have a T on Part B If you choose three blocks at the same time what is the probability that you will not choose a Q Part C If you choose four blocks what is the probability that the first block and second block have W s

What is the value of x F 2 3 6x O 90 07 OOC 12 O 180 E 14x 8 G

6 In the diagram below a rectangle is rotated 360 about line t Describe the shape of the resulting figure Write a formula for the volume of the figure in terms of c AC 3c The rectangle is translated c units from line t and again rotated 360 about line t Sketch the resulting figure Write a formula for the volume of the resulting figure in terms of c C 10 3c

To make the 3d sketch for each of the frames which contain the views in the plan 4

E Which is a correct description of the polygon O It is a concave pentagon because segment AE would extend into the inside of the polygon and it has five sides O It is a convex hexagon because it has six sides and none of the sides would extend into the inside of the polygon O It is a concave hexagon because segment AE would extend into the inside of the polygon and it has six sides O It is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon

2 Determine the volume of the figure below when the pyramid is removed 3 ft 3 ft 3 ft

1 Determine the volume of the figure below Round to the nearest tenth 4 ft 14 ft 8 ft 12 ft 8 ft

6 List the volumes of the figures below from greatest to least 18 yd 14 in 5 in 10 yd 15 yd 19 yd

3 Darren found a punctured basketball in his basement and needs to fill it up with air If the diameter of the ball is 6in how much air will he need to fill the whole ball 3 a 113 in b 345 7 in 3 c 904 3 in 3 d 589 in

15 Label wavelength and amplitude of this wave trequency Wavelength trough 16 How many cycles is the wave in question 14 displaying crest amplitude 17 If the wave above is an electromagnetic wave and it took 2x10 5s what is its frequency and wavelength

Points 2 Question 6 If the scale factor k 0 8 then the original figure is O enlarged O shrunk O congruent O None of the choices

Lesson Posttest Question 7 Points 1 The vertices of a polygon are A 2 2 B 2 4 C 4 4 and D 4 2 and it is dilated by a scale factor 4 Find the dilated coordinates of A O 8 8 O 8 8 O 8 8 O 8 8

The prism below is made of cubes which measure of a centimeter on one side What is the volume OA 27 cubic cm OB 7 cubic cm OC cubic cm D cubic cm Note Figure is not drawn to scale

Find the area of trapezoid STUV Round your answer to the nearest tenth if necessary V 10 in U 18 2 in 18 in 21 5 in 2 24 in inches Submit Answer

Question 5 Find the coordinates of D if the given polygon is dilated by a scale factor of 4 AY 10 5 Points 1 0 O 40 24 40 24 40 8 40 91 A B 10 5 C D 10 X 15

Question 6 If the measure of 21 is 100 find the measure of 2 4 1 80 O 85 O 90 Points 1 O 100 3 2

Question 5 In A PQR O is the centroid and OQ 1 8 cm Find the length of OT Q S Points 2 1 8 cm 1 2 cm 1 0 cm O 0 9 cm 0 6 cm P U T R