Question 18

Question 18 Juan needs a right cylindrical storage tank that holds between 110 and 115 cubic feet of water. Using whole numbers only, provide the radius and height for 3 different tanks that hold between 110 and 115 cubic feet of water. Students can use calculators on this one. Students also need to know that the formula for the volume of a cylinder is: πr2h. Without this knowledge, they probably cannot complete the problem. However, the students are not given the formula for this problem. In each slide, there is one correct answer for the problem. This problem is worth 3 total points: 3 points: all three dimensions are correct 2 points: 2 sets of dimensions are correct 1 point: 1 set of dimensions is correct 0: none are correct. In order to solve this problem the students most likely will use guess and check to get a solution that’s within the values. There is another way the students can narrow their values if they want. This might be confusing so it is up to you to decide if you want to explain it to the students. The formula is V = πr2h, where V is the volume, π is 3.14, r is the radius, and h is the height. One thing the students can do is to find the range of numbers they need to be looking for. To do this, they would take the smallest volume and simplify it down to r2h: 110 = (3.14)(r2)(h) Divide both sides by 3.14 35.03 = r2h You would do the same for the higher end 115 = (3.14)(r2)(h) Divide both sides by 3.14 36.62 = r2h This means that r2h needs to be between 35.03 and 36.62. Somehow, two numbers multiplied together will get you values that you need. Since you can only use whole numbers (no decimals), it is best to look for numbers that multiply to 36. These are all of the possible solutions (where the first number represents the radius and the second number represents the height) 12 * 36 22 * 9 32 * 4 62 * 1 Using these values, you can see if the volume falls within the necessary range.

Question 18 Cont V = πr2h V = πr2h 110 = (3.14) r2h _______ 3.14 _______ 3.14 ____ 3.14 115= (3.14) r2h _______ 3.14 ____ 3.14 35.03 = r2h 36.62 = r2h In order to solve this problem the students most likely will use guess and check to get a solution that’s within the values. There is another way the students can narrow their values if they want. This might be confusing so it is up to you to decide if you want to explain it to the students. The formula is V = πr2h, where V is the volume, π is 3.14, r is the radius, and h is the height. One thing the students can do is to find the range of numbers they need to be looking for. To do this, they would take the smallest volume and simplify it down to r2h: 110 = (3.14)(r2)(h) Divide both sides by 3.14 35.03 = r2h You would do the same for the higher end 115 = (3.14)(r2)(h) Divide both sides by 3.14 36.62 = r2h This means that r2h needs to be between 35.03 and 36.62. Somehow, two numbers multiplied together will get you values that you need. Since you can only use whole numbers (no decimals), it is best to look for numbers that multiply to 36. These are all of the possible solutions (where the first number represents the radius and the second number represents the height) 12 * 36 22 * 9 32 * 4 62 * 1 Using these values, you can see if the volume falls within the necessary range. Any of these set of answers are correct. r = 2; h = 9 r = 1; h = 36 r = 3; h = 4 r = 6; h = 1

Question 18 Cont Possible Solution 1: radius = 1 height = 36 V = πr2h On this page, you are checking the possible solutions that you found from the previous problem. Just because it might look like it works, it is necessary to check to see that it does work. You use the formula, V = πr2h and I used the first set of numbers, 1 and 36. You plug in the values that are known (everything except V), so you get: V = 3.14 * 12 * 36. According to the orders of operation, you do exponents first, so you were square the 1. You end up with: V = 3.14 * 1 * 36. After this, you multiple all of the numbers together and you get that V = 113.04, which is within the range of 110-115.

Question 18 Cont Possible Solution 2: radius = 2 height = 9 V = πr2h On this page, you are checking the possible solutions that you found from the previous problem. Just because it might look like it works, it is necessary to check to see that it does work. You use the formula, V = πr2h and I used the first set of numbers, 2 and 9. You plug in the values that are known (everything except V), so you get: V = 3.14 * 22 * 9. According to the orders of operation, you do exponents first, so you were square the 2. You end up with: V = 3.14 * 4 * 9. After this, you multiple all of the numbers together and you get that V = 113.04, which is within the range of 110-115.

Question 18 Cont Possible Solution 3: radius = 3 height = 4 V = πr2h On this page, you are checking the possible solutions that you found from the previous problem. Just because it might look like it works, it is necessary to check to see that it does work. You use the formula, V = πr2h and I used the first set of numbers, 3 and 4. You plug in the values that are known (everything except V), so you get: V = 3.14 * 32 * 4. According to the orders of operation, you do exponents first, so you were square the 3. You end up with: V = 3.14 * 9 * 4. After this, you multiple all of the numbers together and you get that V = 113.04, which is within the range of 110-115.

Question 18 Cont Possible Solution 4: radius = 6 height = 1 V = πr2h On this page, you are checking the possible solutions that you found from the previous problem. Just because it might look like it works, it is necessary to check to see that it does work. You use the formula, V = πr2h and I used the first set of numbers, 6 and 1. You plug in the values that are known (everything except V), so you get: V = 3.14 * 62 * 1. According to the orders of operation, you do exponents first, so you were square the 6. You end up with: V = 3.14 * 36 * 1. After this, you multiple all of the numbers together and you get that V = 113.04, which is within the range of 110-115.