High School Geometry Questions

pulverized in a ball mill and the resulting powder was digested with various strong resulting solution was evaporated to dryness dissolved in dilute hydrochloric acid and separated from interferents by ion exchange chromatography The resulting solution containing an unknown amount of Pd II was then diluted to 50 00 mL with pH 3 5 buffer Ten milliliter aliquots of this analyte solution were then transferred to six 50 mL volumetric flasks A standard solution was then prepared that was 1 00 10 5M in Pd 11 Volumes of the standard solution shown in the table were then pipetted into the volumetric flasks along with 10 00 mL of 0 01 M arsenazo III Each solution was then diluted to 50 00 mL and the absorbance of each solution was measured at 660 nm in 1 00 cm cells Volume Standard Solution mL 0 00 5 00 10 00 15 00 20 00 25 00 A660 0 216 0 338 0 471 0 596 0 764 0 850 a Enter the data into a spreadsheet and construct a standard additions plot of the data b Determine the slope and intercept of the line J G Sen Gupta Anal Chem 1967 39 18 DOI 10 1021 ac60245a029

27 A a daki O merkezli emberin ap 3 cm dir AC ve BD kiri leri E noktas nda kesi mekte ve m CEB a dir O 18 2 2 E 8 C AB DC 2 cm oldu una g re cosa ka t r A C 1 1 D E 5 9

Solve for x Round to the nearest tenth if necessary H 5 4 16 x G

Calculate the following a 8 b Use permutations to find the probabilities medals will be given to the 1st place 2nd place and 3rd place winner Suppose 3 of the 8 finalists are from There are 8 finalists in the 100 meter dash at the Olympic Games At the end of the 100 meter dash 3 the United States and that all finalists are equally likely to win 3 What is the probability that the United States will win all 3 medals in this event 4 What is the probability that the United States will win no medals in this event

HW Complete problems 1 7 for independent practice 1 Calculate the following 4 2 Calculate the following 7 3 When you are finished check the solutions with your teacher 3 There are 9 students entering the school district s science project with all students having an equal chance of winning There are medals for 1st 2nd and 3rd place In how many different ways can the medals be awarded to students 4 There are 7 unique names in a bowl In how many orders can 2 names be chosen Hint The word orders implies that each unique order of two names is counted as a possibility OX

4 There are 15 Jolly Ranchers in a jar containing 3 blue 3 red 3 green 3 yellow and 3 purple 3 Jolly Ranchers are chosen at random from the jar What is the probability that all 3 chosen Jolly Ranchers are blue Leave your answer as a simplified fraction Hint Follow the 3 step model in Your Turn 3 Step 1 is set up for you Step 1 How many ways can you choose 3 lolly Ranchers in a jar containing 15 Jolly Ranchers This is n S n S 15C3 Step 2 Step 3

HW ework Complete problems 1 7 below for independent practice When you are finished check the solutions in the back of the textbook Find the number of combinations 1 In a standard deck of cards there three royal cards Jack Queen and King How many different combinations of these three cards are there Keep in mind that there are four of each royal card 2 There are 10 applicants for four Computer Programming positions In how many ways can you possibly hire four people 3 There are 13 players on the Volleyball team Six players are actively on the court at any given time How many team arrangements are possible 4 There are 7 ice cream flavors to choose from How many different combinations of triple scoops are possible

Your Turn Find the probability using permutation with repetition 1 There are 2 mystery books 2 romance books 2 poetry books to be randomly placed on a shelf What is the probability that the mystery books are next to each other the romance books are next to each other and the poetry books are next to each other For example MMRRPP 2 The school jazz band has 4 boys and 4 girls and are randomly lined up for a yearbook photo Find the probability of getting all of the boys grouped together

Pernside Nying 3 You have a set of 10 cards numbered 1 to 10 You choose a card at random Event A is choosing a number less than 5 Event B is choosing an even number Calculate the probabilities of the following a P A d P A S 5 1 b P B 3 A 2 4 B 6 e P BC 7 10 8 TOWER 9 VELL c P ANB 4 You roll a 6 sided number cube Use the complement to determine the probability of not rolling a 4 12ES140 SE 5 A bag contains 2 red 5 blue and 3 green balls A ball is chosen at random Use the complement to determine the probability of not choosing a red ball Optional Complete problems 1 9 11 13 15 18 19 23 26 odd from your textbook on separate lined paper

14 12 The method developed in Problem 14 11 was used for the routine determination of iron in 25 0 ml aliquots of groundwater Express the concentration as ppm Fe in samples that yielded the accompanying absorbance data 1 00 cm cell Calculate the relative standard deviation of the result Repeat the calculation assuming the absorbance data are means of three measurements c 0 068 e 1 512 d 1 009 f 0 546 a 0 143 b 0 675

14 11 A standard solution was put through appropriate dilutions to give the concentrations of iron shown next The iron 11 1 10 phenanthroline complex was then formed in 25 0 mL aliquots of these solutions following which each was diluted to 50 0 mL The following absorbances 1 00 cm cells were recorded at 510 nm Fe II Concentration in Original Solutions ppm 4 00 10 0 16 0 24 0 32 0 A510 0 160 0 390 0 630 0 950 1 260

13 11 The equilibrium constant for the conjugate acid base pair HIn H OH 0 In is 8 00 x 105 From the additional information in the following table a calculate the absorbance at 430 nm and 600 nm for the following indicator concentrations 3 00 10 M 2 00 10 M 1 00 10 M 0 500 10 M and 0 250 10 4 M b plot absorbance as a function of indicator concentration Species HIn In Absorption Maximum nm 430 600 Molar Absorptivity 430 nm 8 04 10 0 775 X 10 600 nm 1 23 x 10 6 96 10

HW Complete problems 1 6 below f 1 Find the surface area of the sphere below 2 ft 4 ft When you are finished check the solutions in the back of the 3 Find the surface area of the sphere below 12 8 km 5 Find the surface area of the sphere below Give your answer in terms of 2 Find the surface area of the sphere below 3 1 m 4 Find the surface area of the sphere below 23 4 mi 6 Find the surface area of the sphere below Give your answer in terms of 6 m tional Complete problems 2 3 7 9 10 12 13 15 from your textbook on separate lined paper for extra actice When you are finished check the odd problems for solutiona

Your Turn 2 A basketball is a sphere 29 5 inches in circumference A baseball is a sphere of circumference 9 0 inches How much material is needed to make a basketball Use 3 14 for fr Round to the nearest tenth 1 How much material is needed to make a basketball Hint C 2mr solve for r 2 How much material is needed to make a baseball Hint C 2mr solve for r

3 Find the volume of the square pyramid below Lesson 18 2 1 2 point 9 7 ft 10 ft or 7 ft 4 Find the volume of the cone below Lesson 18 3 1 2 point 10 ft A 8 ft 9 ft 5 Find the volume of the composite figure below Leave your answer in t notation for this problem Lesson 18 3 2 points 3 16 ft Find the volume of the sphere below Lesson 18 4 1 point 10 ft Find the volume of a hemisphere that has a diameter of 26 inches Lesson 18 4 1 point

Fill in the following table by writing the formulas for the perimeter and circumference of the given shapes and finding each shape s actual perimeter or circumference 7cm One sticlan 4cm Shape Polygons 3cm 4cm 11cm Circle 12 in 3cm 3cm 9 7cm Formula 2 AB AH 2 EF FG 4 CD 201 2 7 4 267 3 4 4 2 4 Testfemur sin 722 20 16 8 500m 2 TT 2TTX12 Trova 75 39 inch istorana Actual

Lesson 19 3 Homework HW Complete problems 1 6 below for independ 1 Find the surface area of the regular pyramid below A 7 in 15 ft 6 9 in 12 km When you are finished check the solutions in the back of the t 7 in 3 Find the surface area of the regular pyramid below 10 ft 5 Find the surface area of the cone below 26 8 km 2 Find the surface area of the regular pyramid below 11 mm 8 mm 8 mm 4 Find the surface area of the cone below 13 4 km 6 km 6 Find the surface area of the cone below 8 in 9 8 in Optional Complete problems 5 6 8 9 11 12 from your textbook on separate lined paper for extra pract When you are finished check the odd proble

Lesson 19 2 Checkpoint Checkpoint below Once you have completed the above problems and checked your solutions complete the Lesson Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 You want to reuse an old cookie tin can into a new decorative tin by spray painting the surface Find the surface area of the following cylinder below Use 3 14 for Round to the nearest tenth 6 in Dunich Butter Condi 10 in 2 If one 11 oz spray paint can provide coverage for up to 864 square inches will you have enough for two coats Explain your reasoning

N Your Turn 2 Find the surface area of each composite figure Use 3 14 for m Round Hint Scomposite prism surface area cylinder lateral area 3 cm 9 cm 9 in 2 cm 5 in 5 cm 4 cm 3 in 3 in 5 in 7 in 3 7 mm 0 3 mm 6 mm

Your Turn Find the surface area of each regular pyramid 1 10 2 6 cm 18 cm EXPLAIN 1B Finding the Surface Area of a Pyramid Read the section below and complete the following activity adapted from Lesson 19 3 If only the height altitude of a square pyramid is given one can use the Pythagorean theorem to determine the slant height The slant height of the square pyramid is the hypotenuse of the right triangle formed by the height and half the base length Recall the Pythagorean theorem formula which tells us that the relationship between the legs and the hypotenuse of every right triangle is a b c where a and b are the legs and c is the hypotenuse Finding the Surface Area of a Regular Pyramid if the slant area is not given Step 1 Find the slant height if it is not given Step 2 Find the lateral area RO Altitute Slant height

3 13 in Your Turn Find the surface area of each regular pyramid Round to the nearest tenth if necessary 1 2 8 ft 6fthed 8 in 8 in right Comp Leave your 6 ft 6 ft EXPLAIN 3 Finding the Surface Area of a Cone Read the section below and complete the following activity adapted from Lesson 19 3 A cone is a solid that has a circular base and a single vertex A right cone is a cone whose axis is perpendicular to the base The surface area of a cone is calculated by adding the lateral area to the base To calculate the lateral area of a right cone the slant height I must be known The slant height of a right cone is the distance from any point on circle of its base to the vertex see figure to the right It is not the same as the height of the cone becord ACCOGLODOG

The surface Your Turn Each aluminum can is a right cylinder Find the total amount of aluminum needed to make the can Leave your answer in terms of 1 15 cm 6 cm 2 Pas 80 mm 72 mm

3 The volume of the cone is given Show the work necessary to find that the volume of the cone is V 78 776 3 mi Use 3 14 for I Show the work 28 mi lup 100 mi 4 Find the volume of the cone be wel stumises 14 m 14 m

Your Turn Find the volume of each composite figure 1 16 m 16 m 10 m 4m 5m 2 8 ft 8 ft 8 ft

the volume he cylinder to the right has radius of 2 cm and height of 10 cm Give our answer in terms of it

5 Find the volume of the cone below 10 cm La 10 cm 6 Find the volume of a cone that has a height of 9 inches and a diameter of 12 inches Use 3 14 for and round to the nearest tenth 7 Find the volume of the composite figure Use 3 14 for 7 and round to the nearest tenth The dimensions of the cylindrical conical tank are as follows The radius of the cylinder and cone 17 inches Height of the cylinder 50 inches Height of the cone 32 inches The volume of the cylinder and the cone is given Show the work necessary to find the volume of the composite figure a Show the work to find the volume of the cylinder is V 45373 in b Show the work to find the volume of the cone is V 9679 6 in c Use what you know about composite figures to estimate the volume of the cylindrical conical tank Optional Complete problems 2 5 7 9 10 15 23 from your textbook on separate lined paper for extra practice When you are finished check the odd problems for solutions at the back of the fouthal

shapes 7cm 4cm Shape Polygons 3cm 3cm 4cm 11cm Circle 12 in 3cm 7cm Formula One sticky note is a two dimensional shape like all the previous shapes Describe or draw the shape you would get if you took a lot of sticky notes and stacked them perfectly on top of each other In this credit you will be learning about three dimensional shapes which are created by stacking many two dimensional shapes on top of each other like sticky notes Thinking about how a three dimensional shape is made may help you throughout the credit

Find the volume of each cone 1 Find the volume of the ice cream cone in cubic inches Use 3 14 for and round to the nearest tenth 2 Find the volume of the cone Use 3 14 for and round to the nearest tenth 24in 3 9 in

The gift box is a right prism Find the total amount of paper needed to wrap the box Do not count overlap 1 18 in 5 in 5 in

Your Turn Find the volume of each sphere Use 3 14 for and round to the nearest tenth 3 A spherical water tank has a diameter of 27m How much water can the tank hold to the nearest cubic meter U T 609M 3800 4 The diameter of an NBA basketball is about 9 inches How much air can it hold in cubic inches SPA

Find the volume of the composite figure Round to the nearest tenth 1 30 cm 15 cm 12 cm

Find the volume of each pyramid 1 A piece of pure silver in the shape of a rectangular pyramid has the dimensions shown below What is the volume of this piece of pure silver 2 5 cm 1 5 cm 1 5 cm

2 Find the volume of each figure 1 1 cm 4 cm 3 cm 5 cm 2 cm 4 cm

Given NQ is the bisector of LMNP and ZNMQ ZNPQ Prove A MNQAPNQ M N Q P

Read the question and type your response in the box provided On circle C shown below the measure of ZBCA is 104 C B Enter the measure of ZBDA in degrees

on Pizza You are ordering pizza and you have two choices a slice of pizza from an extra large pizza with a diameter of 22 inches or an entire personal size pizza that has a diameter of 6 inches VS The slice costs 4 95 and the personal size pizza costs 3 75 Assuming that the extra large pizza is cut into 8 equal slices will you get more pizza for your money by buying one slice of the larger pizza or by buying the personal size pizza 1 Find the area of the slice of pizza Use 3 14 for T Round to the nearest hundredth 0 5 point 2 Find the area of the personal size pizza Use 3 14 for I Round to the nearest hundredth 0 5 point

8 Find the value of x in the figure below Lesson 15 4 0 5 point 21 14 27 9 In the circle mBC B E x 38 and mAD 146 What is mzAED Lesson 15 5 1 point 10 Answer the following about the given circle Lesson 15 4 15 5 a If mQR 80 and mQS 150 what is m P 0 5 point

S 70 T U 220 V 19 from your textbook on separate lined paper blems for solutions at the back of the textbook

1 A circular swimming pool has a diameter of 20 feet To the nearest square foot what is the smallest amount of material needed to cover the area of the surface of the pool Use 3 14 for T

For 13 14 give your answer in two forms 1 in terms of rr and 2 using 3 141 the nearest tenth 13 Find the arc length of AB Lesson 16 2 1 point 80 7 in 285 B 14 Find the sector area of the figure below Lesson 16 3 1 point 10 m

arning Goal from Lesson 16 1 16 2 and 16 3 can determine the relationship between an arc intercepted by an angle and the radius can determine arc length and describe radian measure in terms of proportionality I can determine and apply the formula for the area of a sector 11 The diameter and center of circle C are shown Use 3 14 for 7 Round to the nearest a What is the circumference of circle C 0 5 point b What is the area of circle C 0 5 point How I Did Circle one a 50 12 Convert the following degrees into radians Leave your answer in terms of Lesson 16 2 0 5 point each b 125 I got it I m still learning it 18 in

Which pizza is the better buy Explain in words and calculate the cost per square inch of pizza to jus decision 1 point

you have completed the above problems and checked your solutions complete the Lesson Checkpoint below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 Find the area of each sector Give your answer in two forms 1 in terms of 7 and 2 using 3 14 for it Round all answers to the nearest tenth 270 15 mi 2 Find the area of each sector Give your answer in two forms 1 in terms of and 2 using 3 14 for I Round all answers to the nearest tenth 90 13 in

Lesson 16 2 Homework HW Complete problems 1 8 below for independent practice For 1 6 leave your answer in terms of 1 Convert 120 into a radian measure When you are finished check the solutions in the back of the textbook 3 Convert 45 into a radian measure 5 Convert 5 into a radian measure 10 yd 7 Find the arc length Round to the nearest tenth 90 2 Convert 90 into a radian measure For 7 8 use 3 14 for T Round to the nearest tenth 4 Convert 20 into a radian measure 6 Convert 300 into a radian measure 8 Find the arc length Round to the nearest tenth 5 m 60 Optional Complete problems 5 7 13 15 21 22 from your textbook on separate lined paper for extra practice

the area of each sector Give your answer in two forms 1 in terms of and 2 using 3 14 for To the nearest square foot what is the area watered in Example 2 as the sprinkler rotates through a semic

Lesson 16 2 Checkpoint Once you have completed the above problems and checked your solutions compl below Complete the Lesson Reflection above by circling your current understanding of t For 1 2 use 3 14 for mr Round to the nearest tenth 1 Find the arc length of minor arc AB 3 in 120 B LABC is a central angle in a circle with center B The length of the radius is 13 km and mzABC 45 What is the length of minor arc AC hint create your own diagram

Try This Find the measure of the missing arc or central angle for the following Find the measure of the missing angle 125 a olifol 100 The measure of the central angle is 100 b Find the measure of the missing arc 92 The measure of the arc is 92

Turn ert each angle measure to its equivalent radian measure Leave your answers in terms of 90 5

for 1 The minute hand of a clock is 8 inches long To the nearest tenth of an inch how far does the tip of the minute hand travel as the time progresses from 12 00 to 12 45 10 8 11 12 6 5 7

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