3D Geometry Questions and Answers

James sees a car at the dealership for 23 000 base price 1 400 premium interior 1 500 navigation touch screen and 2 000 smart traffic sensors If his current vehicle is worth 8 000 and he s offered a 80 trade in rate what is the total cost of the car after the 1 100 destination fee A 29 000 B 22 600 C 12 800 D 21 000

e Thinking Consider a line x y z 1 2 4 t 3 4 5 te R and the plane What would the intersection between and the plane be Show your thinking e g algebraic work diagram

of each sector Round your answers to the nearest tenth 23 1059

3 You work for a company that makes toy marbles The radius of the most popular marble is 0 3 inches The volume of a marble is given by the formula V where 3 14 ch out of every d a Rounded to the nearest tenth of a cubic inch what is the volume of glass needed to make one of the most popular marbles b What volume of glass is needed to make 105 marbles

43 9 km h 12 7 km km Area 81 9 km A 12 4 km C 10 4 km B 11 9 km D 9 1 km

Christmas ornament in the shape of a sphere has a diameter of 5 5 inches If the mass of the ornament is opounds the density is 9 8 A 0 003 B 0 022 C 43 55 D 348 45 9 W to answer 8 and 9 8 A Inches per pound B Inches per pound C Pound per inch D Pound per inch

13 reflection across y x E 3 2 D 4 3 C 2 4 B 0 2 A D 0 3 C 2 4 B 4 2 E 1 2 B D 3 4 C 4 2 B 2 0 E 2 3 C D 3 4 C 4 2 B 2 0 E 2 3 P D 4 3 C 2 4 B 0 2 E 3 2 formation

1 Directions Find the following arc measures J 3 5 0 127 G F N K D 104 K L L M E 67 This is M mJL mJML mDE mFE mDEF mCFD mDFE II 2 page mKL mLON mOM mKNL mNL 2 4 U 44 T Y 55 X U A D 164 B C V Z 108 S R 25 W mBC mABC mTQ mQR mTS mSQR mRQT II mXVW mVW mYWU II mYU mXW

Finding the Area of a Trapezoid To find the area of a trapezoid you can use a h b b 5 6 9 units D b b 6

6B 28 Given the quadrilateral on the right Create a circle that touches each vertex Identify the center and radius of the circle you created Write the equation of the circle you created 104 47 4 32 3 N 40 A K

5A 5B 24 A contractor is making a toy model grain bin Suppose the two dimensional figure is rotated bout the vertical axis Each small square in the grid represents 1 square foot a 5A Sketch the three dimensional solid that would be formed b 5B Find the volume of the toy model

8 Name the angle in 4 different ways 2 D7

ROOF ACC LITA Mentify and une relationships with angles segments lines and polygons in a circle CAJ The are from A to 8 NOT passing through C measures 50 degrees Select ALL the bue statements A Angle BCA measures 50 degrees Angle BCA measures 25 degrees C Angle BOA meatures 50 degrees D The from B to Chot passing through A measures 180 degrees E Angles C80 and CAD are congruent DAIS Quadrilateral ABCD is shown with the given angle measures Select ALL true statements A Angle A measures 10 degrees The measure of angle A and 0 must add to 180 degrees CAngle A measures 55 degrees D Angle measures 55 degrees E Angle D measures 40 degrees DA Find the measure of the remaining angles of quadrilateral WXYZ D C NM 125 40 PT

INDEPENDENT PRACTICE RO 5 Three balls are packaged in a cylindrical container as shown below The balls just touch the top bott sides of the cylinder The diameter of each ball is 13 cm If the diameter of the cylinder is 13 cm what is the volume of the space around the balls

10 The mass of the figure below is 55 lbs Determine the density of the figure to the nearest tenth UNITS 2 in 2015en ort of sugi 13 in

3 A basketball has a diameter of of the ball is 3 pounds determine the density of the ball 10 lbs cm a 174 5 b 0 006 c 1395 3 d 0 001 lbs cm3 lbs cm lbs cm3 er the em ure

5C 6 Draw two solids that are not identical but that have the same volume

3 5B 3 A superhero action figure has a volume 1500 cm The figure is dilated to create a store display The volume of the dilated figure is 45 000 cm 3 What was the approximate scale factor of the dilation

SC 45 Select ALL shapes that have a volume of 36 cubic units S E 3T F 3 F A 3T C 6 Draw two solids that are not identical but that have the same volume 3x D G

SA 2 Draw the cross section resulting from the intersection of the solid and the given plane Draw HERE Draw HERE Draw HERE

Trapezoid ABCD is a cross section of a lampshade The diagonals of trapezoid ABCD are congruent and the measure of ZD 66 What is the measure of ZB B m B C 66 D

Decide whether quadrilateral ABCD with vertices A 1 3 B 4 2 C 2 4 and D 3 1 is a speci quadrilateral Select all names that apply O parallelogram rectangle O rhombus square

8 Change the following by the specified percentage Increase 240 by 15 PONO

You Try Find the missing side length Tell if the side lengths form a Pythagorean triple Explain Ex 4 Ex 5 15 15 12

What is the ratio for the surface areas of the rectangular prisms shown belo given that they are similar and that the ratio of their edge lengths is 8 5 16 A 512 125 B 25 64 C 64 25 D 125 512 24 5 10 15

rectangular box shown in the figure has dimensions 10 x 6 x 2 a 10 b 6 c 2 Approximate the angle formed by a diagonal of the base and a diagonal of the 6 x 2 side Round your answer to two decimal O a number 8

Determine the shaded area of sector POM P 0 4cm A 0 67 cm B 1 2 cm C 2 4 cm P 9 67 cm 54 M

22 m VOLUME SURFACE 24 6 m 22 m

c y y 3 y 25 y X Construct the phase plot If the phase plot does not exist select the graph of y dy dt dy dt tattit y y dy dt dy dt HW H

Consider the plane which passes through the three points 3 5 8 0 7 5 and 0 8 3 Find the vector normal to this plane which has the form 1 00

Find the x intercepts of the following parabola y 4x 8x 12 A 2 0 3 0 OB 1 0 3 0 OC D 2 0 6 0 6 0 4 0

A hollow toy with the dimensions shown in the figure is to be stuffed with rigid foam What is the maximum amount of foam that can be stuff into the toy Round your answer to two decimal places Assume that both parts are stuffed and the foam does not expand or contract 4 inches OA 52 46 cubic inches OB 67 02 cubic inches C 83 78 cubic inches O D 112 15 cubic inches 12 inches

Select one Om BDC 86 Obm BDC 43 Om BDC 107 Od m BDC 73 150 A What is the m BDC F 64 B D

SOHCAH TOA mnemonics device for remembering right triangle trig ratios Sine is ratio of sides Opposite over Hypotenuse B cos 32 1 Which equation associates an acute angle to a valid ratio of side lengths A sin 380 AB C tan 90 d ale ale le cl D sin 52 1 11 III A I only B III only C I and II D II and III SOH CAH TOA AB Cosine is ratio of sides Adjacent over Hypotenuse 2 Given the right triangle ABC below which of the following is equal to b sin A cos B tan A Tangent is ratio of sides Opposite 38 B a over Adjacent 40 ft 52 B b 25 ft

What is the volume of the original sculpture What is the volume of the new sculpture How much greater of a volume is the new sculpture Select one O a The original sphere s volume is 33 ft the new sphere s volume is 904 ft and the new sculpture s volume is approximately 27 times the volume of the original O b The original sphere s volume is 33 ft the new sphere s volume is 904 ft and the new sculpture s volume is approximately 9 times the volume of the original Oc The original sphere s volume is 268 ft the new sphere s volume is 7235 ft and the new sculpture s volume is approximately 27 times the volume of the original

A tank in the shape of a hemisphere has a diameter of 6 feet If the liquid that fills the tank has a density of 91 7 pounds per cubic foot what is the total weight of the liquid in the tank to the nearest full pound

Elizabeth was playing with a spinner that has 3 equal areas numbered 1 2 and 3 Elizabeth spun the spinner 100 times and 23 of the 100 spins came up as a 3 She wanted to see how likely a result of 23 threes in 100 spins would be with a fair spinner so Elizabeth used a computer simulation to see the proportion of threes in 100 spins repeated 100 times assuming a probability of of spinning a 3 Create a 95 confidence interval based on the data from the simulation to the nearest hundredth and state whether the observed proportion of threes is within the margin of error of the simulation results 1 Mean 0 331 SD 0 048 0 2 0 25 ooooo oooooo 0 3 0 35 Proportion of Threes 0 4 0 45 0 5 Note don t use percents for the interval or sample proportion The confidence interval based on the simulation is observed proportion of threes of is spinner s simulation so the of the fair

Round Tree Manor is a hotel that provides two types of rooms with three rental classes Super Saver Deluxe and Business The profit per night for each type of room and rental class is as follows Room Type I Type II Super Saver Deluxe Business 30 Rental Class 20 35 30 40 Type I rooms do not have high speed Internet access and are not available for the Business rental class Round Tree s management makes a forecast of the demand by rental class for each night in the future A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class The demand forecast for a particular night is 160 rentals in the Super Saver class 60 rentals in the Deluxe class and 50 rentals in the Business class Round Tree has 100 Type I rooms and 120 Type II rooms a Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types Is the demand by any rental class not satisfied Explain If demand materializes as forecast there will be rooms not reserved in th Select Super Saver Deluxe Business b How many reservations can be accommodated in each rental class Super Saver Deluxe Business ss

Consider AXYZ in the figure below The perpendicular bisectors of its sides are TS US and VS They meet at a single point S In other words S is the circumcenter of AXYZ Suppose VS 66 YZ 82 and ZS 110 Find XS UZ and VY Note that the figure is not drawn to scale X VO Y S T DU Z XS UZ VY X A 0 U

Find the area of quadrilateral ABCD with vertices A 0 4 B 4 1 C 1 3 and D 3 0 20 square units 5 square units 5 5 square units 25 square units

An equilateral triangle is rotated around an axis bisecting the triangle What shape is formed triangular prism cone diamond triangular muramid

A plane slices through a cone parallel to the base What shape is the cross section circle triangle oval square

What set of reflections would carry trapezoid ABCD onto itself 1 point A BO T 9 2 C Ox axis y x y axis x axis Ox axis y axis x axis Oy x x axis x axis Oy axis x axis y axis x axis T D 3 2 27

Find the volume of this object Use 3 for Volume of a Cylinder V r h 4 ft 9 ft 5 ft 5 ft 5 ft Volume of a Rectangular Prism V lwh V ft

Each hemisphere of a beach ball has a volume of 281 250 cm What is the radius of the ball in cm 152

2 Determine the volume of the figure below given their Faull 000

6 A cylindrical pringles can was full of pringles If the cylinder is 13 cm tall and has a diameter of 14 cm and the volume of the pringles in the can is 1632 cm determine the volume of the empty space in the can

E 10 ft A 261 8 B 785 4 C 916 3 5 ft 5 ft 5 ft A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure above Of the following which is closest to the volume of the grain silo in cubic feet

3 The pill below is a cylinder with a hemisphere on top and a hemisphere on bottom What is the vo 4 cm Hint a hemisphere is half of a sphere the shape below if the radius is 2 cm and a 1 r

Fwd the S 24 cm We 714 What is the volume of the shape V 28 938 24 cm V 2 712 96 cm V 7 234 56 cm V 3 617 28 cm V 603 19 cm