3D Geometry Questions and Answers

1 point The planes dy 22 10 and 4 4x 5 23 are not parallel so they must intersect along a line that is common to both of them The ver parametric equation for this reis Z t

What is the vertex of the parabola x y 6 6 4

P Complements What is the complete complement of event of randomly drawing a single card from a shuffled deck and drawing a card with a heart on it Cards have four types of cards club diamond heart or spade il a la alia alla alla alla alla THAT THIT Drawing a card with a club Drawing a card with a diamond Drawing a card with a spade Drawing a card with a club spade or diamond 7

Continuous Probability A person is waiting to hear a certain song on the radio to try to win a contest for concert tickets The radio station manager promises that they will play the song randomly once sometime between 5 00pm and 10 00pm The person had to work and do some chores and was only able to listen to the radio from 6 00pm to 7 30pm What is the probability that the person heard the song during the time they listened 26 30 32 36

7 In the diagram below which of the following does not make pllq a 21 and 25 are congruent corresponding angles b 23 and 26 are congruent alternate interior angles c 27 and 28 are supplementary linear pair angles d 23 and 25 are supplementary same side interior angles t

If two parallel lines are cut by a transversal what is the relationship between alternating interior angles

Find the sine cosine and tangent of the referenced angle Write the ratio as a fraction Trigonometric Function Ratio sin 27 cos 27 tan 27

Points P 6 20 and Q 12 8 are the endpoints of the diameter of circle K Find the center of the circle 3 6 9 14 3 10 6 4

Question A cone is packaged inside a cardboard box To ship it the company puts Styrofoam peanuts around the outside of the vase to keep it stable What is the approximate volume must be filled by the Styrofoam peanuts 212 cubic inches 233 cubic inches 362 cubic inches 536 cubic inches 7 in 10 in 7 in

A company needs to determine the volume of a cereal box to determine the amount of cereal it can hold Which the most appropriate geometric solid that would describe the cereal box prism pyramid cone cylinder 7333

Q9 A B C and D are points on the circumference of a circle The line EF is a tangent to the circle a Find the size of angle x b Find the size of angle y 73 B Q10 A03 A B and Care points on the circumference of a circle and is the centr 2 2 3

a Sketch a graph of each vector valued function r t Acos 1 B sin t b F t 3 1 1 2t 1 t

L Moving to another question will save this response Question 9 Calculate the area of the outlined figure below The figure is made up of a rectar Each segment on the grid represents one inch Round your final answer to tenths if rounding is necessary

Cole has a cylinder that fits within a cube The height and diameter of the cylinder are each equal to x Each side of the cube is also equal to x Cole wants to know the volume of water that can be poured inside the cube yet outside the cylinder Which expression will help Cole solve for this volume

3 Harvey is at the store buying some hummus He has two options available to him One is a cylindrical tub that is 2 inches tall and has a radius of 3 inches The other is a rectangular box that is 4 inches tall and has a square base with a perimeter of 20 inches What are the volumes of the two containers If the tub costs 6 and the box costs 10 which container is a better deal

Let A 2 3 1 and B 4 1 2 and C 6 2 3 Find the equation of the line in parametric form assing through C that intersects AB is perpendicular to AB

What is the volume of the trough 9 ft 3 ft 7 ft 29 cubic feet 32 cubic feet 64 cubic feet 74 cubic feet 8 ft A B 2 ft

The diagram shows the measurements of a frame into which concrete is poured to make steps The steps are shaped like rectangular prisms Which expressions can be used to find the volume of concrete used for the steps 00000 16 in 6 in 6 in 14 in 6 x 16 x 8 7 x 14 x 8 6 x 16 x 6 14x16x7 6x16x6 14 x 7 x 6 6x6x14 16x6x7 6x6x13 8 x 16 x 7 13 in

1 An open i e it has no top rectangular box with volume 8 m has a square base Express the surface area of the box as a function of the length of a side of the base 8 points

warm up When you have finished your work A parabola with equation y x 13 2 intersects the line with equation y 4 in the xy plane at two points M and N The length of bar MN is which of the following

14 The following figure shows a right prism and a right pyramid The height of each figures is 9 2 cm The bases of the prism and the base of the pyramid are the exact same seven sided polygon The area of the 7 gon is 23 cm Determine the volume of the prism and the volume of the pyramid 9 2 cm

5 Simplify the expression below 12s 68 48 681 4s 27 48 8 12

a G Part A Based on the graph how many zeroes does the polynomial function f z 3x 6x 8z have Answer 7 4 2 only 4 0 2 3 6 Part B What are the zeroes of the above polynomial function

5 SAT Question Systems of Equations In the xy plane the lines y 3x 5 and y 2x 10 intersect at the point h k What is the value of k

a solid is the circle x 2 y 2 4 Find the volume of t pendicular to the x axis are squares

3 Match each building with the geometric shapes that Cone

complicated Prisms Anas Al Tibawi T 8

1 Consider the solids shown below HEADSH Which of them are polyhedra Which of them are prisms Which of them are cylinders but not prisms Which of them are pyramids Which of them are cone pyramids Which of them are Platonic solids

Question 15 1 point Consider the following measures shown in the diagram with the circle centered at Point A Determine the approximate arc length of CB i e Find the length of the arc intercepted by a central angle of 148 and a radius of 3 meters 9 32 m 19 85 m 15 50 m 7 75 m B A 148 3 m Figure may not be drawn to scale

Suppose a carpet costs 2 a square foot to purchase and install How much would it cost to carpet the shaded region where AB 7 ft HC 2 ft CJ 3 ft F G 4 ft and GD 2 ft Assume all non obtuse angles are right angles Be sure to mention assumptions related to the application in your 6 point discussion

Find the amplitude and period of the function y 1 cos x amplitude period Sketch the graph of the function y y 0 4 0 2 VV 0 2 0 4 X 2 0 2 0 1 5 1 0 0 5 y 1 5 1 0 0 5 0 5 1 0 1 5 y 1 5 1 0 0 5 0 5 1 0 1 5 2 0 X

Which of the below figures is a net of the pyramid shown at the right Figure may not be drawn to scale

2 Express in simplest radical form 8 3

Espa ol In the triangle below suppose that m2 K 2x 8 m L 5x 4 and m m M x Find the degree measure of each angle in the triangle xo 2x 8 M 5x 4 L m2K m2 L m M 0 X S 8 Aa

10 12 14 yd 8 km 14 yd 12 km 10 km 11 13 3 2 cm 8 ft

18 20 12 in 10 mi 12 in 20 mi 10 in 19 2 cm 6 cm 3

6 12 yd 8 yd 5 yd 7 9 0 7 in 11 yd 10 yd

Use the circle to answer the following In the circle mPS 120 and m QR 162 P 120 Q A 78 162 What is the value of x B 91 C 182 Ho D 39 S R

equation of the ellipse with center 10 9 a focus at 10 15 10 19

Identify the number of vertices edges and faces of the polyhedron Use your results to verify Euler s formula OV 4 E 9 F 7 4 9 7 2 OV 4 E 7 F 5 4 7 5 2 OV 6 E 9 F 5 6 9 5 2 OV 6 E 7 F 3 6 7 3 2

ve one pair of supplementary angles and one pair of vertical angles shown in the figure below 1 2 4 3 5 6 8 7 1 m a Supplementary angles 40 and 40 40 and 40 b Vertical angles X

Does the isometric view represent the object Assume there are no hidden cubes Front nt the object Ono yes O yes yes O no no Top Side

Which of the following shows all the six orthographic views of the object Assume there are no hidden cubes O O O Top Top Top TILI Front Bottom TIL Fret Korisn lack Bottom TIL Front Back Back Left Left Left aught Right

Classify the figure Identify its vertices edges and bases L O P T M R N rectangular prism vertices L M N O P Q R S edges rectangle LOPQ and rectangle MNSR bases LM MN NO OL LQ QP OP QR RS SP MR and NS rectangular prism vertices L M N O P Q R S edges LM MN NO OL LQ QP OP QR RS SP MR and NS bases square LOPQ and square MNSR rectangular prism vertices L M N O P Q R S edges LM MN NO OL LQ QP OP QR RS SP MR and NS bases rectangle LONS and rectangle PQRM rectangular prism vertices L M N O P Q R S edgos LM MN NO OL LQ QP OP QR RS SP MR and NS bases rectangle LMNO and

Identify the three dimensional figure that can be made from this net rectangular pyramid O cone O square pyramid O triangular pyramid

Identify the three dimensional figures that can be made from this net O triangular pyramid O trapezoidal prism O rectangular prism square pyramid

Identify the area of the rhombus 13 cm 110 cm 1 O A 240 cm A 120 cm O A 221 cm O A 130 cm

1 Find parametrizations for the following 3 dimensional curves a A circle of radius 2 centered at the origin in the plane x y b A piecewise linear curve from 0 0 0 to 1 0 1 to 1 1 1 This curve is the shortest path between opposite corners of a unit cube as shown in the diagram below c A curve that goes from the north pole to the south pole of a sphere of radius 1 so that

Volume of Spheres Practice Key Find the volume of each figure Round your answers to the nearest hundredth if necessary 1 2 Q 3 5 7 6 yd 5m 10 mi 19 km e 8 4 mi 1 ft Date 22 cm 8 mi

Kayla 7 9 18 mi 18 mi 7 cm K 3 cm 1 par 8 10 10 km 12 km 8 c 6 cm