3D Geometry Questions and Answers

Consider the following 2 x y z 6 Sketch a graph of the plane Label any intercepts If an answer does not exist enter DNE X intercept x y z Y intercept x y z 2 intercept x y z

Prove that the lateral surface area of a right circular cone with height h and base radius r S ar a 0 b 0 h 0

Represent a b using the parallelogram method Use the Vector tool to draw the vectors complete the parallelogram method and draw a b To use the Vector tool select the initial point and then the terminal point Show Transcribed Text To use the Vector tool select the initial point and then the terminal point Move Vector 7 6 5 4 3 2 7 6 5 4 3 2 1 1 0 T 2 3 4 Undo y 1 2 3 Redo x Reset 4 5 6 7 X

Question 1 15 points Given the circle centered at point A shown in the diagram has a radius of 6 cm in length determine the area of the circle 6 square cm 9x square cm 12 square cm 36 square cm A 6 cm B

Read the problem below and answer An oil company inherits a T shaped oil tank The tank is 10 feet thick throughout the entire tower One cubic foot of oil equals 7 48 gallons How many gallons of oil can be stored in the oil tank Based on your work on the previous page how many gallons of oil can be stored 22 feet 38 feet 50 feet

Read the problen An oil company inherits a T shaped oil tank The tank is 10 feet thick throughout the entire tower One cubic foot of oil equals 7 48 gallons How many gallons of oil can be stored in the oil tank What formula s do you need to solve this problem Write the formula s to the right and solve the problem 22 feet 38 feet 50 feet

An oil company inherits a T shaped oil tank The tank is 10 feet thick throughout the entire tower One cubic foot of oil equals 7 48 gallons How many gallons of oil can be stored in the oil tank a In your own words what is this problem about b What important information do you have in this problem 22 feet 38 feet 50 feet

The diameter of a circle is 18 feet What is the length of a 150 arc 150 Give the exact answer in simplest form feet T d 18 ft Olc

Edgar has a spherical balloon that has a diameter of 18 centimeters Dale has a spherical balloon that holds 4 times as much air as Edgar s balloon What is the diameter of Dale s balloon Show your work here Hint To add the nth root symbol V type root

Ingrid is baking a cake and has mixed 370 mini chocolate chips into the batter Ingrid pours the batter is poured into a rectangular pan that measures 5 inches by 14 inches After poured the batter measures exactly 1 8 inches in height What is the density of chocolate chips in the batter Round your answer to two decimal places as necessary

A horizontal slice through a 3D solid produces a circle similar to the one shown What 3D solid may have been sliced

A cylindrical glass has a diameter of 1 inches and is 9 inches tall Suppose the faucet dispenses water at a rate of 1 cubic inches per second How long does it take to fill the glass 60 Enter your answer as a decimal rounded to two places Show your work here Hint To add the nth root symbol yno

A vertical slice through a 3D solid produces a trapezoid similar to the one shown What 3D solid may have been sliced Ve

Question 4 25 points A pyramid with a regular hexagon base is shown Each side of the hexagon measures 4 cm and the height of the pyramid is 6 cm Using the provided measures find the approximate volume of the solid 83 1 cm 98 2 cm 166 3 cm 2494 cm om Figure may not be drawn to scale

Question 3 25 points A cone is shown with the following measures A radius of 9 cm A height of 12 cm Determine the volume of the cone 324 x cm 432 cm 624 x cm 972 8 cm 12 cm 9 cm Figure may not be drawn to scale

Find the volume of the prism shown in the diagram using the provided measures Figure may not be drawn to scale 196 cm 256 cm 288 cm 320 cm 15

15 tan Z O 20 A OB O C N OD 5 Y 13 12 SES X

Question 3 13 points Saved Find the total surface area of a rectangular prism that has the dimensions 4 cm x 6cm x 8cm Figure may not be drawn to scale 160 cm 192 cm 208 cm 288 cm Acm 8cm

The trapezoid J K L M is a diration of the tropezoid JKLM What is the scale factor of the dilation mplify your answer and write it as a proper fraction an improper fraction or a ole number 5 2

6 Apples are catapulted off of the stand into the crowd 5 4 3 10 9 B y f x 0 25x 2x 5 2 5 44 6 7 9 10 a What is the maximum value Explain what it represents in this situation using the x and y values in your explanation b What are the y and x intercepts of the graph represent and what do they represent

1 Given the Polar Equation r 3 sin 20 a Perform the three symmetry test for the equation 3 points b Sketch the graph of polar equation by plotting the point 3 point

Transform the following quadratic form to principal axes 9x 17x 6x x 36 Express x2 in terms of new variables yi 12 Show each step of the solution in detail Justify and explain your answer

L K P Your Answer 0 M If mON 13 degrees and m LPM 35 degrees Find mLM Answer N

143 217 57 1 19 Find the measure of x Fo 143 CLindsay Bonden 2017

Given that x is the measure of the major arc BC find the value of x A 64 C B

A straw is placed inside a rectangular box that is 10 inches by 8 inches by 9 inches as shown If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner how long is the straw Leave your answer in simplest radical form 9 in I I I 10 in 8 in

Date res of Graphs Notes Function Or Not a function Domain Range Y Intercept Relative Min Relative Max Absolute Min Absolute Max Continuous or Discrete Per Figure 4

The diameter of a sphere is 2 ft What is the sphere s volume Round to the nearest tenth 4x x A B 33 5 ft C 16 8 ft C 4 2 ft 810

CCR be the curve from 0 6 0 to 3 3 27 along the intersection of the surfaces y 6 and z Find a parametrization a for C 1 R a t a with

The base of a solid is the region in the zy plane between the the lines y x y 3xz z 2 and x 4 Cross sections of the solid perpendicular to the z axis and to the zy plane are squares The volume of this solid is

Denver After driving for 3 hours she was only 100 miles east from Denver Assume that Julia drove at a constant speed during the trip Let be a function that gives Julia s position east from Denver measured in miles after having driven for hours a Determine a rule for the function b Interpret the meaning of 16 and then find its value if it exists c Interpret the meaning of 141 and then find its value if it exists d Determine a rule for e Construct a graph for

What is mZF F 2x m F G 6x 76 H I

Use 3 14 and round the volume to the nearest meter 5 m 8 m Figures 8 m 6 m 7 m 80 m 410 m 240 m 1231 m

9 Do the following for the function g x X a Express the slope of the secant line in terms of x and h 1 1 1 and at x 1 What value does msec approach as h approaches 0 100 b Find msec for h rh 2 10 1 c Find the equation for the secant line at x 1 with h 100 d Graph g and the secant line found in part c on the same viewing window a Type the slope of the secant line in terms of x and h msec Simplify your answer

he similar triangles find the unknown measurement 150 12 75 6 180 10 150 75 330 x MULTIPLE CHOICE QUESTION Which of these is NOT a correct proportion fa the two triangles 150 75 350 75 330 150 330 2 150 330 75 75

4 Which solid has a volume that is 3 times the volume of a cone with the same base and height A prism B cylinder Csphere

5 If the circumference of the circular base of a cylinder is doubled how does the volume of the cylinder change A The volume is doubled B The volume is tripled The volume is eight times larger The volume is quadrupled

A plane slices horizontally throug a sphere dividing it into two hemispheres Which term best describes the cross section of the plane and the sphere cylinder B circle triangle Doval

A cup of hot water is left out to cool The water is currently 19 C above room temperature If the heat difference decreases by 5 every minute what will the difference be in 13 minutes If necessary round your answer to the nearest tenth

A MBA Crystal Ball a All Radii b All the Chords c All the Point on the circle d All the Diameters Figure 2 B Name the Parts of the circle

3 A forester is trying to estimate the height of a tree Standing 43 feet from the base of the tree the forester determines that the angle between the ground and the top of the tree is 52 The following drawing is not to scale Using a scale of 1 cm 5 feet draw the situation to scale Assume that the tree is perpendicular to the ground Use your drawing to approximate the actual height of the tree 43 ft 52

The two polygons shown are similar Determine the value of y and z Q X y yo Z R W P 6 S Z 10 9 12 Z X 118

Evaluate the triple integral II xy dV where E is the solid tetrahedon with vertices 0 0 0 9 0 0 0 4 0 0 0 4 E

A straw is placed inside a rectangular box that is 8 inches by 10 inches by 9 inches as shown If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner how long is the straw Leave your answer in simplest radical form 9 in 8 in 10 in

Find the following for the vectors v 4i 5j 3k and a u 4i 5j 3k v u lvl lul b the cosine of the angle between and V u c the scalar component of u in the direction of V d the vector proj

A 3D printer will produce the solids A and B see the figure below A B 40 Both solids have the same height of 10 cm and all horizontal cross sections of both solids are disks of radius 2 cm Then printing the solid A requires more plastic than the solid B printing the solid A requires less plastic than the solid B printing the solid A requires the same amount of plastic as the solid B there is not enough information to make a conclusion comparing the amount of plastic

4 Plot the graph of g x over the domain 5 6 and range 9 5 as follow a f x x 9 x 3 and f x x 9 x 3 with line thickness 4 and colour magenta b Show symbol to mark the discontinuity if any with colour green and symbolsize 30 c f x 4 x 3 with point colour magenta symbol solidcircle and symbolsize 30 d Label and display x 9 y 4 and x 9 on the graph paste the screenshot of map

5 You are trying to drive to the mall However the road to get there is closed and you are required to take the detour Because of the detour how many mors miles did you have to drive A 6 miles B 13 miles C 17 miles Road Closed

2 Which function g x shows the parent function f x vertically stretched by a factor of 3 reflected over the x axis and translated right 2 units and translated up 4 units 2 4 g x 3 x2 4 A g x B 1 3 g x 3 x 21 4 13 9 a 12 21 4 g x

Draw an arbitrary pentagon Mark the points counterclockwise Mark the size of the angles by selecting the Angle measurement tool and clicking in the middle the pentagon Calculate the angle sum in the input field and display the value in a text box decide yourself with which accuracy the size of the angles must be specified Change the shape of the pentagon by dragging one of the corners and check that angle sum does not change Insert a picture of the construction in the Word document Also show how you can prove what the sum of the angles in the pentagon is provided that we proved that the sum of the