Day 151 Bellringer. 2. Find the volume of a cone whose diameter is equal to its height which measures 16 in. (Write answer to 4 significant figures)

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1 Day 151 Bellringer 1. Find the volume of a cylinder, whose radius and height are 8 in and 11 in respectively. (Write answer to 4 significant figures) 2. Find the volume of a cone whose diameter is equal to its height which measures 16 in. (Write answer to 4 significant figures) Use the following information to answer questions 3 and 4 A cylindrical tank has an internal diameter of 7.2 ft while its thickness is 0.8ft. 3. Find the capacity of the tank in cubic feet if it is 4.5 high. (Write answer to 4 significant figures) 4. What is the volume of the thickness of the wall of the cylinder? (Write answer to 4 significant figures) 5. What would be the volume of a cone whose height which is twice the diameter is 24 in. (Write answer to 4 significant figures) HighSchoolMathTeachers@2017 Page 1

2 Day 151 Bellringer Answer Key Day 151: in in in in in 3 HighSchoolMathTeachers@2017 Page 2

3 Day 151 Activity 1. Fold a manila paper so that you form a pipe of between 1 in to 2 in diameter. 2. Use the paper to hold the pipe in position while maintaining its diameter. 3. Cut out a manila pipe with 3 in to 4 in high. 4. Slant the pipe and cut the remaining manila pipe so that its height is the same as the one in 3 above. 3in 4 in 1in to2 in 5. Mount the two pipes on a flats surface and fill the upright manila pipe with sand. 6. Take out the sand from the upright pipe and without adding or removing any, pour it into the mounted slant pipe. 7. What do you notice about how each pipe is filled with the sand? Make a conclusion. 8. Why do you think you got the results as they are in 7 above? HighSchoolMathTeachers@2017 Page 3

4 Day 151 Activity In this activity students will work in groups of at least 4. They will come up with two cylinders and verify that their volume is the same using Cavelieri s Principle. Each group will require a manila paper (A3 size or more), a flat surface, sand (at least 4 cups), a cutting tool (razor blade, a pair of scissors or a similar tool), a tape and a ruler. Answer Keys Day 151: 1-6. No response 7. The manila pipes are filled with the same amount of sand. Thus, the volume of the two are equal 8. The pipes are cut from the same pipe, hence, at any given point of their cross section is equal. Hence by Cavelieri s principle, the volume of the two pipes is equal. HighSchoolMathTeachers@2017 Page 4

5 Day 151 Practice Use the following information to answer questions 1 19 We are give that the tops and well as the bottom parts of the two images lies on the same plane. We also have that The plane having ABC is the same plane having lin KPLQM and is parallel to the two planes. The ratio of ULto LT is 4 1. We would like to apply Cavelieri s principle is applicable to prove that the volume of the two figures are the same. All answers must be interms of t and π where applicable. E t T A t B C t K P L Q M D 2t V U 2t Cross section details A B C K P L Q M 1. Find the value of UL and LT 2. Find the value of DB 3. Find the value of EB. HighSchoolMathTeachers@2017 Page 5

6 Day 151 Practice 4. Find the value of AB. 5. Find the area of the circle on the cross section of the hemisphere. 6. Make a similarity statement in triangle UVT then identify the proportional sides 7. Find the value of PL 8. Find the area of the smaller circle on the cross section of the cylinder. 9. Find the area of the larger circle on the cross section of the cylinder. 10. Find the area of the cross section of the cylindrical object. 11. Compare the area of the cross sections in 10 and 5 above. 12. What does your answer in 11 above with respect to Cavelieri s Principle s hypothesis imply. 13. Compare the volume of the hemisphere with that of the other object. HighSchoolMathTeachers@2017 Page 6

7 Day 151 Practice 14. Find the volume of the cone 15. Find the value of the cylinder 16. Find the volume of the spehere using Cavelieri s principle. Show your working. 17. If the height of the hemisphere were 6.24 in, using the formula,what would be its volume interms of π? 18. If the height of the hemisphere were 2r in (where r is the radius), using the formula,what would be its volume interms of π? 19. Comment in what the answer in 18 imply. 20. Find the volume of the following figure. Write your answer in 4 significant figures. 7 in 25 in HighSchoolMathTeachers@2017 Page 7

8 Day 151 Practice Answer Keys Day UL = 0.2t, LT = 0.8t t t t πt 2 sq. units 6. Triangle PLT and VUT are similar The proportional sides are VU and PL, UT and LT, and VT and PL t πt 2 9. πt πt They are equal 12. The hypothesis is satisfied hence, we can apply Cavelieri s principle. 13. Volume of the hemisphere = volume of the cylinder volume of the cone 14. V = π 3 t3 15. V = πt V = πt 3 π 3 t3 = πt 3 (1 1 3 ) = 2 3 πt π πr3 19. This would be the volume of the sphere cubic in HighSchoolMathTeachers@2017 Page 8

9 Day 151 Exit Slip Find the volume of the slant figure if the two are enclosed in between two parallel planes 5 in 3 in HighSchoolMathTeachers@2017 Page 9

10 Day 151 Exit Slip Answer Keys Day 151: in 3 HighSchoolMathTeachers@2017 Page 10

11 Day 152 Bellringer 1. Calculate the volume of the spheres with the following diameters. a) 5 in b) 12 ft 2. Calculate the radii of the spheres with the following volumes. a) in 3 b) 15 cubic feet 3. Water is pumped into a empty tank at a rate of cubic inches per second. If the tank is filled after one hour, calculate the volume of the tank. HighSchoolMathTeachers@2017 Page 11

12 Day 152 Bellringer Answer Key Day 152: 1. a) in 3 b) cubic feet 2. a) 21 in b)1.530 ft in 3 HighSchoolMathTeachers@2017 Page 12

13 Day 152 Activity 1. Read and record the initial level of water in the graduated cylinder. 2. Put the three ball bearing into the measuring cylinder with water. 3. Read and record the new level of water in the graduated cylinder. 4. Subtract the initial level from the new level and divide the result by three to get the volume of one ball bearing. 5. Calculate the diameter of the ball bearing. 6. Using a vernier caliper, measure the diameter of the ball bearing. Is the diameter close or equal to the result in 5 above? HighSchoolMathTeachers@2017 Page 13

14 Day 152 Activity In this activity students will estimate the radius of a ball bearing. Students will work in groups of at least three and each group is required to have three ball bearings, a graduated cylinder filled half way with water and a vernier caliper. Answer Keys Day 152: 1. Different responses 2. No response 3. Different responses 4. Different responses 5. Different responses 6. Different responses but the answer should be close or equal the answer in 5. Yes. HighSchoolMathTeachers@2017 Page 14

15 Day 152 Practice 1. A fish pond build in form of an hemisphere is 1 full of water. If the diameter of the pond is 4 30 ft, calculate the volume of the remaining water needed to completely fill the pond. Use the following information to answer questions 2-3. A company makes plastic 32,000 beads in a day. Each bead has a radius of 0.2 in. 2. Calculate the volume of plastic contained in one bead. 3. Calculate the volume of plastic used by the company in one day. 4. Calculate the volume of gas which can fill a ball with a radius of 5.5 in. Use the following information to answer questions cubic feet of water was poured into a spherical pot. The pot became 3 full after the water 4 was poured. 5. Calculate the radius of the pot. 6. Find the volume of the pot. Use the following information to answer questions 7-8. A mason uses one bag of cement to mix 17 cubic feet of concrete. He uses a spherical concrete mixer with a radius of 1.6 ft to mix the concrete. 7. Calculate the volume of the concrete mixer. HighSchoolMathTeachers@2017 Page 15

16 Day 152 Practice 8. Find the number of bags he puts in the concrete mixer. Use the following information to answer questions A farmer uses three spherical water tanks each of radius 3 ft in his farm. To save space, he wants to replace them with one big spherical water tank that has the volume of the three tanks combined. 9. Calculate the volume of one smaller water tank. 10. Calculate the total volume of water that can be contained in all the three smaller tanks. 11. Find the radius of the tank that the farmer should buy. 12. A man wants to design a spherical oil tank that can hold 50 pints of oil. Find the radius of the tank. (1 pint = cubic inches) 13. A baker bakes spherical cakes each of radius 1.5 in. Find the volume of one cake. 14. A trader buys 1 cubic feet of paraffin at one kerosine. If he fills her spherical tank which has a diameter of 6.4 ft with kerosine, how much will she pay? 15. A cuboid measuring 4 in by 5 in by 7 in is moulded into a sphere. Calculate the radius of the sphere in 3 of molten steel is used to make 10,000 ball bearings. Calculate the radius of one ball bearing. HighSchoolMathTeachers@2017 Page 16

17 Day 152 Practice Use the following information to answer questions A spherical water container with a radius of 12 in is half way full of water. When 30 snooker balls are put into the water in the container, the water level rises until it is completely filled. 17. Calculate the volume of water in the container. 18. Find the volume of 30 snooker balls. 19. What is the volume of one snooker ball. 20. Find the radius of one snooker ball. HighSchoolMathTeachers@2017 Page 17

18 Day 152 Practice Answer Keys Day 152: ft in in in ft 6. 1 ft ft bag ft ft ft in in dollars in in in in in in HighSchoolMathTeachers@2017 Page 18

19 Day 152 Exit Slip The volume of water in the graduated cylinder is 3.9 in 3. After a spherical ball bearing was immersed in the water, the volume of the water rised to 4.8 in 3. Calculate the radius of the ball bearing. HighSchoolMathTeachers@2017 Page 19

20 Day 152 Exit Slip Answer Keys Day 152: in Page 20

21 Day 153 Bellringer 1. Find the area of a circle with a radius of 3 in. 2. Calculate the volume of a cylinder with a radius of 3 in and a height of 5 in. 3. Calculate the height of a cylinder with a radius of 3 in and a volume of 85 cubic inches. 4. Calculate the radius of cylinder with a volume of 150 cubic inches and a height of 6 in. 5. Find the volume of a cylinder with a radius of 4 ft and a height of 7 ft. HighSchoolMathTeachers@2017 Page 21

22 Day 153 Bellringer Answer Key Day 153: in in in in ft 3 HighSchoolMathTeachers@2017 Page 22

23 Day 153 Activity 1. Using a pencil, mark the level of water in the jar. 2. Put the piece of the stone into the jar. 3. Using a pencil, mark the new level of water in the jar above the first mark. 4. Using the ruler, measure the distance between the two marks. 5. Calculate the volume of the water that rose. What is the volume of the piece of the stone. HighSchoolMathTeachers@2017 Page 23

24 Day 153 Activity In this activity students will estimate the volume of a small stone. Students will work in groups of at least three and each group is required to have a piece of a stone, a pencil, a ruler and a transparent cylindrical jar or a beaker half way full of water. Answer Keys Day 153: 1-3. No response 4. Different responses 5. Different responses Different responses but students should follow the method of calculating the volume of a cylinder using the result in 4 as the height. HighSchoolMathTeachers@2017 Page 24

25 Day 153 Practice 1. A man wants to buy a water tank with a volume of 550 ft 3 that will fit on a square stand measuring 10 ft by 10 ft. If he decides to by a tank with a radius of 5 ft, calculate the height of the tank. 2. A cylindrical oil tanker has a length of 17 ft and a diameter of 6 ft. Calculate the volume of the tanker. Use the information below to answer questions 3-4. A student wanted to know the volume of a tank. He tied a rope around the tank and found that the circumference of the tank was 37.7 ft. He then measured the height of the tank and found that the tank was 10 ft heigh. 3. Find the radius of the tank. 4. Calculate the volume of the tank. Use the information below to answer questions 5-6. A man dug a pit latrine 10 ft deep and with a diameter of 5 ft. The soil evacuated was then sold for 10 cubic feet at 0.5 dollars to another man who makes brinks. 5. Calculate the volume of soil evacuated. 6. How much money did the man pay for the soil? 7. A water pipe has an internal diameter of 0.25 ft and a length of 20 ft. Calculate the volume of water contained in the pipe. 8. Find the volume of steel used to make a steel water pipe 20 ft long with an internal diameter of 0.22 ft and an external diameter of 0.3 ft. HighSchoolMathTeachers@2017 Page 25

26 Day 153 Practice Use the information below to answer questions A cylindrical water cooler bottle with a diameter of 1 ft and a height of 1.8 ft is filled using a cylindrical jag with a height of 1 ft and a diameter of 0.4 ft. 9. Calculate the volume of the water cooler bottle. 10. Calculate the volume of the jag. 11. How many jags of water will fill the cooler bottle? Use the information below to answer questions A company buys 10 cubic inches of candle wax at 0.10 dollars to make two types of candles. Type A has a length of 10 in and a diameter of 3 in.type B has a length of 7 in and a diameter of 2 in. In one day the company makes 1000 type A candles and 850 type B candles. 12. Calculate the volume of candle wax contained in type A candle. 13. Calculate the volume of candle wax contained in type B candle. 14. Calculate the volume of candle wax used by the company per day. 15. Calculate the cost of candle wax per day. 16. A trader sells honey in cyndrical cans of radius 3 in and height 6 in. A can has honey upto a height of 2 in. How much honey is missing in the can. HighSchoolMathTeachers@2017 Page 26

27 Day 153 Practice Use the information below to answer questions A jar of radius 4 in and height 7 in contains water upto a height of 4 in. When a piece of a stone is inserted, the water rose upto a height of 6 in. 17. Calculate the volome of the water that was initially in the jar. 18. Find the volume of the stone. 19. Calculate the volume of concrete needed to make a culvert of length 12 ft and with internal radius 2 ft and external radius of 2.5 ft. 20. A jar with a radius of 1.5 in and a height of 6 in is full of water. The water is then transferred to a beaker of radius 3 in. Calculate the height of the water in the beaker. HighSchoolMathTeachers@2017 Page 27

28 Day 153 Practice Answer Key Day 153: 1. 7 ft ft ft ft ft dollars ft ft ft ft jags of water in in in dollars in in in in in HighSchoolMathTeachers@2017 Page 28

29 Day 153 Exit Slip A company makes two types of cylindrical steel rods; type A and type B. Type A has a diameter 3 in and a length of 40 ft. Type B has a diameter of 5 in and a lenth of 40 ft. The cost of making one cubic feet of a rod is 0.5 dollars. In one day the company made 200 type A rods and 150 type B rods. Calculate the cost of production in that day. HighSchoolMathTeachers@2017 Page 29

30 Day 153 Exit Slip Answer Keys Day 153: dollars Page 30

31 Day 154 Bellringer 1. Use the figure below to answer the questions that follow. 13 in 5 in a) Find the vertical height of the cone. b) Calculate the volume of the cone. 2. Calculate the volume of a cone with a radius of 4 in and a vertical height of 10 in. 3. Find the volume of each of the following pyramids. a) A pyramid with a square base of 10 in and a vertical height of 12 in. b) A triangular based pyramid with sides 12 in, 8 in and 10 in and a vertical height of 7 in. HighSchoolMathTeachers@2017 Page 31

32 Day 154 Bellringer Answer Key Day 154: 1. a) 12 in b) in in 3 3. a) 400 in 3 b) in 3 HighSchoolMathTeachers@2017 Page 32

33 Day 154 Activity 1. Using a ruler, measure the diameter of the funnel and divide it by two to get the radius of the funnel. 2. Measure the vertical height of the funnel. 3. Calculate the volume of the funnel. 4. Hold the outlet of the funnel with your finger and fill it with water. 5. Transfer the water in the funnel to the graduated cylinder. 6. Record the readings of the graduated cylinder. Are readings equal or close to the volume of the funnel? HighSchoolMathTeachers@2017 Page 33

34 Day 154 Activity In this activity students will find the volume a conical funnel. Students will work in groups of at least four and each group is required to have a conical funnel, a graduated cylinder, a ruler, and water in a beaker. Answer Keys Day 154: 1. Different responses 2. Different responses 3. Different responses 4. No response 5. No response 6. Different responses but the reading should be close or equal to the result in 3. Yes HighSchoolMathTeachers@2017 Page 34

35 Day 154 Practice Use the information below to answer questions 1 2. A company have been manufacturing perfumes and packing them in pyramid bottles with a square base measuring 4.5 in by 4.5 in and a height of 6 in. The company wants to introduce conical bottles with the same capacity and a diameter of 5 in. 1. Find the volume of one perfume bottle. 2. Calculate the height of the conical bottle that needs to be introduced. Use the information below to answer questions 3 7. A movie theatre sells ice creams in conical and pyramid shaped containers. The conical containers have a radius of 2 in and height of 3 in. The pyramid containers have a rectangular base measuring 4 in by 3.8 in and a height of 7.3 in. In a day they sell 120 conical containers of ice cream and 100 pyramid containers of ice cream. The price of conical and pyramid shaped containers of ice cream is 0.10 dollar and 0.30 dollars respectively. 3. Calculate the volume of the conical container. 4. Calculate the volume of the pyramid shaped container. 5. Calculate the total volume of ice cream sold in one day. 6. How many conical containers can fill one pyramid shaped container with ice cream. 7. Calculate the total sales per day. HighSchoolMathTeachers@2017 Page 35

36 Day 154 Practice Use the information below to answer questions A water bucket has a shape of a frustum. The bottom and top radii of the bucket are 5.5 in and 6.7 in respectively. The height of the bucket is 1.8 ft. This bucket is filled with water using a smaller container which is the shape of a frustum with a height of 6 in. The bottom and top radii of the smaller container are 2 in and 4 in repectively. 8. Calculate the volume of the bucket. 9. Calculate the volume of the smaller container. 10. How many containers will fill the bucket with water. Use the information below to answer questions A company makes two types of earrings; conical and pyramid shaped earrings. The conical earrings have a radius of 0.2 in and a height of 0.3 in. The pyramid shaped earings have an hexagonal base of sides 0.1 in and a height of 0.3 in. 11. Find the volume of a conical earring. 12. Find the volume of hexagonal earring. 13. If the company makes 1000 earrings of each type in a day, calculate the total volume of earrings produced in one day. 14. A water storage tank is in the shape of a frustum with botton and and top radii of 4 ft and 6.5 ft respectively.the height of the tank is 8 ft. Calculate the total volume of the tank. HighSchoolMathTeachers@2017 Page 36

37 Day 154 Practice Use the information below to answer questions A funnel has a slant height of 5 in and a radius of 4 in. A student wanted to know the number of funnels of water that can fill a square based pyramid container with sides of 10 in and a height of 9 in. She closed the nozzle of the funnel and filled it with water then transferred the water to the pyramid container. She did this a number of times until the pyramid container was filled. 15. Find the vertical height of the funnel. 16. Calculate the volume of the funnel. 17. Calculate the volume of the pyramid container. 18. How many funnels filled the pyramid container. Use the information below to answer questions A soccer team wanted to build a pyramid monument as a souvenir after winning tournament. They agreed on building a pyramid monument with a rectangular base measuring 4 ft by 5 ft and a height of 6 ft. 19. Find the volume of concrete used in building the monument. 20. Find the volume of concrete that they could have added had the team decided to build a conical momument of radius 4 ft and height 5 ft. HighSchoolMathTeachers@2017 Page 37

38 Day 154 Practice Answer Keys Day 154: in in in in in containers dollars in in containers in in in ft in in in funnels ft ft 3 HighSchoolMathTeachers@2017 Page 38

39 Day 154 Exit Slip A roof of a house is pyramid shaped. For uniformity the owner wants to place a water tank that is pyramid shaped with the same colour as the roof just beside the roof. The water tank should hold 480 ft 3 of water and should have a base of 12 ft by 12 ft. Calculate the vertical height of the tank. HighSchoolMathTeachers@2017 Page 39

40 Day 154 Exit Slip Answer Keys Day 154: 10 ft Page 40