Geometry Questions

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

Find the value of x Write your answer as a decimal N 29 X O Zo xo Y

For each scenario write whether it involves surface ar How long would it take to paint the outside of a house ft How much dirt would it take to fill in a hole he space OUTSIDE BD figure How much water needed to fill a pool How many yards of fabric needed to How much glass needed to build a greenhouse How much cardboard is needed to make a cereal box How much air needed to fill a tire ft How much coffee can fit in a cup The space INSIDE a 3D figure How much wrapping paper needed to wrap

A bundle of fabric will cover approximately 1800 square inches Mr Longo wants to cover all the outside surfaces of his rectangular file cabinet with fabric A diagram of the file cabinet is shown below What is the least number of bundles of fabric Mr Longo needs to buy to cover his file cabinet What formula should he use to help him decide a 1 b 2 C 3 d 4 e 5 1111 480 28in 26in 48in

Find the value of x Write your answer as a decimal 122 D A 41 to B

Find the measure of arc RPQ P S 39 O 42 Q The measure of arc RPQ is R degrees

Write an equation of the perpendicular bisector of the segment with the endpoints 3 5 and 9 1 y

Find the measure of ZC Write your answer as a decimal B 100 C A m C 45 D

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

Find the area of a circle with a diameter of 16 meters Round your answer to the nearest hundredth of a square meter The area of the circle is about square meters

Which of the following trigonometric ratios are correct b A 40 Ocos 40 cos 40 sin 40 sin 40 tan 40 X b a X 64 b X X b X tan 40 X a 33

You are planting a garden in the shape of an equilateral triangle as shown in the diagram You want to find the area of the garden to determine how much topsoil you will need 8 ft 60 8 ft 30 A Substitute the values of b and h in the formula A 2 8 ft 2 b h for the area of the garden

Determine the value of x in the diagram 6x X 3x 3x 6x

he mayor wants to build a new gas station so that it is the same distance from the three main roads in town At whi bint of concurrency should the gas station be built O centroid O circumcenter O incenter O orthocenter

5 Find the measure of the indicated angle to the nearest degree a 64 c 24 b 66 d 19 45 101

Find the value of b Round your answer to the nearest tenth 24 b B 40 20 C

Find the areas of the sectors formed by ZNMP Round your answers to the nearest hundredth of a square centimet N 10 cm 120 M L The area of the small sector is about on of the large sector is about square centimeters square centimeters