Geometry Questions

10 The mass UNITSI ed assismlinss 490 E ancianochib 26 cha to soste 90 lugnaben 16ans to 2 The figure below is horizontally cut What is the cross section created a Circle b Triangle c Rectangle 1 Dantagon 16 50 eam sr 17 000 b ons needed to cover the entire figure

Answer Review Key Concepts Polygon interior angle sum theorem The sum of the measures of the 180 1 2 where is the number of angles of any n gon is of the polygon

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

DO NOW 1 Kaliyah and Kennedy were given the task to determine the volume of the figure below Their work is below Analyze their work and determine which student correctly solved for the volume of this figure and identify the other student s error Kaliyah s work 1 V Bh 3 6 15 14 1 3 6 210 V 1 V V 420 ft Kennedy s work 1 V Bh 3 x 1 105X14 14 V 3 1 V 45 14 V 210 ft Which student correctly solve for the volume of this figure What was the other student s error 6 ft 14 ft 15 ft

of water is 1 gram per cm3 An object floats in water if its density is less than water s density and it sinks if its density is greater than water s ass 90 grams is in the shape of a sphere with radius 2 5 centimeters Will the lime sink or float in water Explain or show your reasoning

39 36 S 15 cos R cos S sin R sin S tan R tan S 36 39 15 39 15 39 36 39

E B H G Radius Chord Diameter Secant 1111 AB DF GH CD

Give the value of each trigonometric ratio R 39 36 cos R Cos S sin R S 15 T TIT 15 36 36 39 36 15

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

5D 7 A cylindrical cup is 8 centimeters in height When filled to the very top it holds 480 cubic centimeters of water What is the radius of the cup rounded to the nearest tenth Explain or show your reasoning

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

58 4 A pet supply company makes a small bag that holds 2 pounds of dog food They want to make a bag for large dogs that holds 40 pounds of dog food By approximately what factor will the surface area of the bag increase Round your answer to the nearest tenth

x y 6x 4y 4 0 O Circle 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 N 1 OF 2 3 7 Undo 1 2 3 4 Redo 5 6 x Reset 8 9 10

c sin P Q sin P Q cos Q cos P 2 A satellite s distance above the Earth s surface in km in terms of time in minutes is recorded in the table below 60 232 869 54 48 42 550 869 1000 66 100 24 30 Time min Distance km 6 550 18 12 100 232 36 869 550 232 A number of different equations have been determined and are listed below Equation 1 H t 450 cos 42 550 Equation 3 H t 450 sin t 6 550 a Determine if any of the equations are correct and what error s in the incorrect equations b Determine if other equations can be determined that are not listed already 72 78 232 550 Equation 2 H t 450 cos t 18 550 Equation 4 H t 450 sin t 30 550

TU is tangent to OS What is the value of x S 3x 2 2x 7 U

Consider the graph of a transformed secant shown below 9 8 7 6 y 5 4 y 3 2 1 4 3 2 1 0 1 2 3 4 5 6 7 a What is the period of the corresponding sine graph Show Transcribed Text b What is the amplitude of the corresponding sine graph 2 3 4 5 6 G c What is the midline of the corresponding sine graph d Give a formula for the corresponding sine graph e Give a formula for the cosecant function graphed above

5 Use the following image to answer the questions below 60 120 1 m a Based on the picture what properties can you be sure this figure has Think about angles lines and intersectio b Are I and m parallel Explain your thinking What would you need to do to prove that I and mare parallel

is tangent to OW What is XY X Y 20 km 16 km W

The radius of a circle is 6 feet What is the length of a 45 arc 45 r 6 ft

BF is tangent to circle O at point U UA is the circle s diameter Find m FU

Score 30 an a n 1 d 1 1 For each general term write the first 3 terms of the sequence and identify it as arithmetic geometric or neither 4 marks a an 2n 1 b an 3 c an 8n d an 3n 1 2 The general term is given Find the indicated terms for each sequence an n 3 17 and tis b an n n 2 t11 and 135 4 marks

3 mA 57 5 m mAB 650 180 A D 5 ft 65 B m B 9 m c 32 5 OD 68 01 7 Area OD 882 5 115

2 If the measure of LXYZ 70 in C find the measure of ZXCZ X Z C 70 Y

T6A Describe transformations in the plane 6A 9 Rotate the line on the diagram to the right 90 clockwise about the origin Graph and write the equation of the rotated line LT 6B Translate between the geometric description and the equation of circles and parabolas 68 10 What is the center and radius of the circle with this equation B 2 1 y 4 3 2 NM 2 NM 5 PT

3 Miyea is filling up her ice cream cone at the self serve station She wants to fill it up halfway with vanilla and halfway with chocolate If the cone has a height of 4 inches and a diameter of 8 inches how much vanilla ice cream will be in her cone Hint the height and radius are proportional in a cone so if the height is cut in half the radius will also be halved

7 Kendon and Success are playing soccer but are trying to see whose soccer ball is better to use with the most air William s soccer ball has a diameter of 22 cm and Daniel s has a 14 cm radius Whose soccer ball is better to use Why

1 Determine whether each scenario represents surface area or volum a Helium in a balloon b Glazing on a donut c The peel to a banana d Water inside a pool e

Directions Use the area and circumference formulas to find the radius or diameter 7 Find the radius of a circle with an area of 615 75 square kilometers 8 Find the diameter of a circle with a circumference of 15 71 yards 9 Find the diameter of a circle with an area of 415 48 square inches dezsin 11 Find the diameter of a circle with an area of 240 25 square millimeters 10 Find the radius of a circle with a circumference of 125 66 feet 15 Find the circumference of a circle with an area of 1 134 11 square meters Directions Use the information given to find the area or circumference 13 Find the area of a circle with a circumference of 117 feet d sed 12 Find the radius of a circle with a circumference of 45 centimeters Y 20ft 14 Find the circumference of a circle with an area of 676x square millimeters 16 Find the area of a circle with a circumference of 53 41 inches wif nis 20 k OL te t

6 Madison is making a cup holder to go around her school water bottle She s trying to figure out how material she needs to go around the cup Below are the two formulas she was working with SA 2 r h 2 r V r h Which one of them would she need to use and why Circle your formula above then explain your reasoning below ch Thanks to your help she was able to determine which formula She figured out how much space the shape takes up and was now buying material to make her cup holder When working it out she solved that she needs 3 24 rods of material so she purchased 3 rods Her mom told her she needs to purchase one more rod as 3 won t be enough Who is correct Why Use math to justify your answer

2 Mr Mann s cylindrical fish tank has a base area of 102 cm and a height of 12 cm How much water fish tank hold a 114 cm b 1224 cm c 900 cm d 1020 cm b He d like to wrap his fish tank in clear wrapping to prevent scratches If the diameter is 24 cm how much wrapping will he need

68 11 A circle has a center at 4 1 and a point on the circle is located at 2 5 Write the standard form equation that would graph this circle LT BC Use coordinates to work with objects algebraically x y 14x 12y BC 12 Are the lines below parallel Use mathematics to support your claim 10 NM fo 3 11 PT AT

LI SU Solve pr 50 7 A cylindrical cup is 8 centimeters in height When filled to the very top it holds 480 cubic centimeters of water What is the radius of the cup rounded to the nearest tenth Explain or show your reasoning 50 8 The density of water is 1 gram per cm3 An object floats in water if its density is less than water s density and it sinks if its density is greater than water s Suppose a lime with mass 90 grams is in the shape of a sphere with radius 2 5 centimeters Will the lime sink or float in water Explain or show your reasoning

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

SA 1 A student has a rectangular postcard that he folds in half lengthwise Next he rotates it continuously about the folded edge Which three dimensional object below is generated by this rotation A B C D

Find the value of x A xo D 115 47 C B

Pineapple Street intersects Plum Street and Apple Street at their midpoints Your home is at point P You leave your home and jog down Plum Street to Kiwi Street over Kiwi Street to Apple Street up Apple Street to Pineapple Street ove Pineapple Street to Plum Street and then back home up Plum Street How many miles did you jog Apple Street 1 1 miles Pineapple Street 1 3 miles Kiwi Street 2 15 miles Plum Street

Find the length of JM JM G H 12 10 K 15 M N

Find the value of x 15 B X X A C 16 D

In the diagram point P is a point of tangency Find the radius r of OO Q 6 P O 18

ABCD is a parallelogram Which statements are true B 22 9x 2 A 110 3y 2 D Oy is greater than 5x O The product of x and y is greater than 100 O x andy are both factors of 80 0 10 times y is less than 9 times x

Find the exact value of x X 9 4

Find mHK H L 13x mHK MO N J 60 x K

You can calculate the width of the lake using a surveying technique as shown in the diagram Find the width of the lake 115 m W 8 m N 3 X Y 10 m

Find the value of x A D X X 8 E 12 C 6x B

Determine whether each statement is true or false U QT SU R RT RU T 1 27 m RQT m RSU S True O False

Find the circumference of circle L Write your answer as a mixed number or decimal L 112 K 1 75 ft The circumference is feet

Given AE EC for what value of x is quadrilateral ABCD a parallelogram A B 5x E 2x 1 D C

Find the value of x X 24 14 S 7 R X

Which relationship is true for the triangle based on the Law of Sines 18 R O O 110 43 sin 110 18 sin 110 18 sin 110 43 sin 110 43 sin T 43 sin S 43 sin S 18 sin T 18 S 33