Area Questions and Answers

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

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

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

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

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

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

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

Find the exact value of x X 9 4

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

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

Select one O a surface area 492 m O b surface area 616 m O c surface area 570 m O d surface area 463 m 4m 6m 7m 11 m 9m 7m

What is the number of possible outcomes for the tree diagram below A 6 B 3 C 9 D 12 2 3 N 3 3 2 3

A 32 Inch computer monitor is shown X 28 in 32 in What is the height of the screen x in inches 000 Round your answer to the nearest tenth of an inch

7 Find the volume of the roll of duct tape 2 0 cm 4 0 cm VOLUME 1 0 cm

4 4 Yd 3 Yd VOLUME SURFACE 1 C 4 3 Yd 3 Yd

The following two triangles are similar Find the value of y 12 20 5 Your answer 13 B

Determine the perimeter and area of the shape shown below Both rounded regions are semicircles 6 in 6 in Perimeter 49 70 X inches Area 149 10 X square inches Use the button on your calculator to make sure your answer is as accurate as possible Round your answer to the nearest hundredth as needed Question Help Video 1 Video 2

The following two triangles are similar Find the value of x 12 5 Your answer 13 6 B X The following two triangles are similar Find the value of y

Find the surface area of the solid The cylinder and cones are right A C 716 3 m 942 5 m B D 867 1 m 1168 7 m 8 m 6 m 15 m 6 m 8 m

Select the correct answer from each drop down menu 1 inch 4 5 inches 3 inches Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder Based on this assumption volume of the flask is cubic inches If both the sphere and the cylinder are dilated by a scale factor of 2 the resulting vo would be times the original volume

Type the correct answer in the box Assume t 3 14 and round your answer to the nearest hundredth 3 ft 4 ft At the rate of 2 00 per square foot the cost of painting the rectangular board with a semicircular top shown in the figure is

Select the correct answer length of AB Points A and B lie on a circle centered at point O If OA 5 and circumference what is the area of sector AOB Use the value rt 3 14 and choose the closest answer OA 19 6 square units B 39 3 square units OC 7 85 square units OD 15 7 square units

Type the correct answer in the box Round your answer to the nearest whole number A manufacturer makes ball bearings out of molten steel It takes 5 24 cubic centimeters of molten steel to make have a diameter of 1 centimeter ball bearings that ea

Find the area of the shaded region below All measurements are in meters 12 Area 10 4 meters 9

B Grade Results My Activities Tell me what you want to do Q Question 39 Points 2 Triangles PQR and PST are similar to each other Further PQ and PS are given as 8 and 16 units If PR 4 units then find PT and RT P OPT 8 units RT 4 units O PT 4 units RT 4 units O PT 8 units RT 8 units a Ims graderesults com OPT 2 units RT 4 units S

Question 33 Which of the following represents the notation of ray AB O AB O AB O AB Points 2 OAB

Question 30 Points 2 Rectangles are parallelograms with congruent O sides O Obtuse angles O diagonals O Acute angles

Question 27 In the triangle DE is the mid segment Find the length of BC B D Points 2 6 5 cm 6 5 cm O 9 cm 11 5 cm 13 cm E C

Question 23 Find ZQRS if the lines segments PQ and RS are parallel 60 Points 1 90 S O 120 180 120 P R containing the line

Question 20 The two triangles are similar to each other Find the measure of E and G 60 Points 3 B C 60 and 30 O 55 and 30 O 70 and 30 E F G

Question 2 Identify the ray A P OAB O PQ XY Points 1 RS B Q S X R Y

Tert 2 52 28 Three friends decide to go out to eat and then go shopping If there are 5 local restaurants and 4 good stores for shopping how many possibilities are there for their big night out Hint they can only pick one of each Select one a 40 Ob 10 Oc 15 Od 20 A bag contains 10 beads 2 black 3 white and 5 red A bead is selected at random The probability of selecting a white bead replacing it and then selecting a red bead is This is a event

For the rhombus below find the measures of 21 22 23 and Z4 1 2 43 36 m2 1 m 22 m 23 m 24 11 8000 11 0 0 X

Given A EFG RSQ Which statement is true Select one O O EF RS FG SQ EG RQ EF RS FG SQ EG RO EF FG ORE 0 RQ RS SQ EG

Find the area of the parallelogram 4 m F 10 m m 5 5 m 2

Area of a trapezoid 1 2 b1 b2 h Find the area of the trapezoid below Round your answer to two decimal places 20 3 cm 8 9 cm 25 cm Select one O a 730 cm O b 401 8 cm O c 403 17 cm O d 201 59 cm

b The mzBEA 41 3 What is the measure of minor arc BA B ct one a measure of minor arc BA 41 3 E C measure of minor arc BA 97 7 measure of minor arc BA 82 6 d measure of minor arc BA 138 7 41 3

AABC is rotated 180 about the origin and then dilated by a factor of 2 using the point 4 6 as the center of dilation What is the transformation of C 2 4 65432 OR 4 3 N 2 2399 C 2 4 B 5 3 O A C 1 1 O B C 1 0 O C C 1 1 O D C 0 1 A 3 1 2 3 4 5 6

A circus owner wants to place an ATM at a location that is equidistant from the three main tents at points D E and F Which of the following can be used to determine where to locate the ATM O the medians of ADEF O the altitudes of ADEF O the angle bisectors of ADEF O the perpendicular bisectors of ADEF

Determine whether each statement is true or false 113 KL NM M P KL NM 114 N m MPN m LJK True O False O

Select one O a 560 units O b 580 units OC 160 units What is the volume of 14 units Area of base 40 square units 10 units

The diameter of a sphere is 8 units What are the radius and volume elect one a The radius is 4 units and the volume is 803 85 units O b The radius is 4 units and the volume is 267 95 units Oc The radius is 16 units and the volume is 51 445 76 units Od The radius is 16 units and the volume is 17 148 59 units

A cone has a radius of 5 inches and a height of 13 inches If its radius and height were enlarged by a scale factor of 2 5 how much larger would the volume of the new cone be Select one O a 32 5 times larger O b 6 25 times larger OC 12 5 times larger O d 15 625 times larger

Find the angle between vectors 2 6 and 11 7 Select one O a 39 01 O b 72 4 OC 82 04 O d Do not have enough information

MATHEMATICS WRITTEN WORK 1 A Write Draw the correct relation symbol to show the relationship Use a separate sheet of paper 1 AB 4 105 m2 1 6 7 DE 110 S Quarter 4 mZ2 6 B Find the measurement of the missing angles U 70 50 6 T 3 m21 Grade 8 Statements C Directions Complete the two column proof 10 15 Given A LMN where LM IN MN Prove MN IN LM MN LM LN LM LN MN Proof m22 Y 4 ZLPN ZMPN 5 ZLNP ZMPN 6 ZMNP LNM ZLNP 1 IP IN 2 ALNP is an isosceles triangle 3 ZLNPZLPN 8 9 2 FG 5 MS M N Notice that since MN LN and that MN LM then it is obvious that MN LM IN and MN LN LM are true 95 Hence what remains to be proved is the third statement LM LN MN Let us construct LP as an extension of LM such that Lis between Mand P LP LN and A LMN is formed 50 M LM LS 115 MATH SCIENCE ENGLISH MAPEH Reasons Page 5 of 1 By construction 2 3 Base angles of isosceles triangles are congruent 4 5 6 Angle Addition Postulate

14 Find the area of the shaded region 9 cm

Find the surface area of following 6 cm 7 cm 4 cm 12 cm 8 cm 8 cm

5 A rectangular town has an area of 900 miles In the town the reservoirs and ponds have an area of 224 miles If the total number of people living in the town is 6 513 determine the population density ppl mi ppl a 7 2 b 9 6 29 1 c d 0 1 mi2 ppl mi2 ppl mi