VOLUME CALCULATIONS PRACTICE

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Chester Mills
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1 Last Name First Name Professor Date Note: Note: VOLUME CALCULATIONS PRACTICE This is Practice Work. Unless I give this during lecture, this is not due for a grade. I did not give you room on this sheet to do your work. You will need your own paper. RELEVANT EXAM 1 INFORMATION There are no volume calculations questions in Part 1 of the Exam. However, you may be asked to supply the equation for the volume of a rectangular box (memorized information) in Part 1 of the Exam. You must show your work for full credit You must use units through each step. The answer must be numerically correct. The answer must have the exact number of significant digits correct. The units in the answer must match the units in the work. Since there will be a section devoted to writing unit equations and unit factors, you are not required to write both unit factors if and when you have to convert from one unit to another. The Exam will have approximately two or three of these questions. CALCULATIONS INSTRUCTIONS You will usually be instructed to write the equation before you start plugging in values. When you plug in values (measurements), you must recopy significant digits. When you plug in values (measurement), you must include units. Units must be carried through each step. The following criteria must be met for the final answer for full credit: The final answer must be numerically correct. The final answer must have the correct number of significant digits. The units of the final answer must match your work. You must show enough steps in order for me to follow your work. If you have to explain to me what you did in your work after the work has been graded: I either made an egregious mistake (it happens) Use equals signs when you are supposed to. Be sure to circle or box your final answer. I know this is a lot. I know this is different but these are good work habits to get into if you are going to carry on into CHEM 10 and CHEM 11. Page 1 of 10

2 VOLUME EQUATIONS Units of Volume Can be in traditional volume terms: liters, millilters, gallons, quarts, etc Can be in cubic length terms: cubic meters, m 3 ; cubic centimeters, cm 3 ; cubic inches, in 3 ; etc Volume of a rectangular box: Vbox = l w h Part 1 of the Exam: Memorized; you will be expected to be able to regurgitate this equation. Part of the Exam: This equation will be given to you, if needed. Vbox = l w h Vbox represents volume of the box l = length (units are length: cm, m, in ) w = width (units are length: cm, m, in ) h = length (units are length: cm, m, in ) In the lab, this parameter was referred to as thickness. Special Note: Vbox = Area h = A h = l w h Therefore, if you know the l w, you also know the area. Therefore, if you know the area A, you also know the l w Therefore: Vbox = Area height = A h You will be given this equation for all parts of the Exam You will not be asked to regurgitate this equation in Part 1 of the Exam. If you need this equation for Part of the Exam, it will be given to you. For extra credit questions: all bets are off! Page of 10

3 Volume of a sphere: V sphere = ( 4 3 ) ( ) (r3 ) Part 1 of Exam: You will not be asked to regurgitate this equation. Part of Exam: This equation will be given to you, if needed. V sphere = ( 4 ) ( ) (r)3 3 ( 4 ) Self-explanatory: you should be able to plug this into your calculator easily. 3 ( ) Use the x x button on your calculator. Do not plug in (r 3 ) The radius, cubed. When you plug in the radius, make sure that it is the radius (and not the diameter) When you plug in the radius, make sure that you include units and original sigdigs. Relationship between the radius and diameter This information will not be given to you on any section of the Exam. The relationship between the radius and the diameter is considered to be common knowledge if you are in any scientific or medical field. radius = diameter circle OR r = d r (radius) and d (diameter of a circle) are both in units of length: cm, in, feet, miles, etc If you have to convert, do the conversion before you cube the radius. Otherwise, you ll be sorryyyyyyy To avoid confusion, I will use rho (ρ) to symbolize density and the special (d ) to symbolize radius. Page 3 of 10

4 CALCULATIONS INSTRUCTIONS You will usually be instructed to write the equation before you start plugging in values. When you plug in values (measurements), you must recopy significant digits. When you plug in values (measurement), you must include units Units must be carried through each step The following criteria must be met for the final answer for full credit: The final answer must be numerically correct. The final answer must have the correct number of significant digits. The units of the final answer must match your work. PRACTICE PROBLEMS Question 1 A rectangular box has a length of 1.5 m a width of 0.40 meters and a height of 1.50 meters. Follow the instructions below to calculate the volume of the box. 1a) In the box below, write the equation for the volume of a rectangular box. (1 pt all or nothing) 1b) Using the Equation, written in Question 1a, plug in the values and solve for the volume of the box. (7 pt) Question A sphere has a radius of cm. Follow the instructions below to calculate the volume of the sphere. a) What is the radius of the sphere? If you need to calculate it, use the space below to write the equation for the radius of the sphere, and then plug-n-chug. ( x pt) Answer for Question a b) Write the equation for the volume of a sphere in the box provided below. (1 pt) c) Using the Equation written in your answer to Question a, calculate the volume of the sphere. (7 pts) Page 4 of 10

5 Question 3 A sphere has a diameter of 1.00 dm. Follow the instructions below to calculate the volume of the sphere. 3a) What is the radius of the sphere? If you need to calculate it, use the space below to write the equation for the radius of the sphere, and then plug-n-chug. ( x pt) Answer for Question 3a 3b) Write the equation for the volume of a sphere in the box provided below. (1 pt) 3c) Using the Equation written in your answer to Question 3a, calculate the volume of the sphere. (7 pt) Question 4 The volume of a rectangular box is 7.00 dm 3. The length of the box is.4 decimeters. The width of the box is 4.50 dm. Calculate the height (thickness) of the box. 4a) Write the equation for the volume of a box. (1 pt all or nothing) 4b) Use the equation for the volume of the box to determine the height (thickness) of the box. You must show your work. (7 pts) Question 5 The volume of a rectangular box is 450. cm 3. The height of the box is.50 cm. Calculate the area of the box. 5a) Write the equation for the volume of a box. (1 pt) 5b) Rewrite the volume equation from Question 5a so that area is represented. ( pt; a/n) 5c) Use the equation for the volume of the box to determine the area of the box. You must show your work. (7 pts) Page 5 of 10

6 Answers/Solutions Question 1 A rectangular box has a length of 1.5 m a width of 0.40 meters and a height of 1.50 meters. Follow the instructions below to calculate the volume of the box. 1a) In the box below, write the equation for the volume of a rectangular box. (1 pt all or nothing) Vbox = l w h (1 pt) 30 s, max: all levels. 1b) Using the Equation, written in Question 1a, plug in the values and solve for the volume of the box. (7 points) Vbox = Mastery (A) = 1 min Competence (C) = min l w h No, you don t have to re-copy the equation, but you d be surprised at how well it helps you. Vbox = (1.5 m) (0.40 m) (1.50 m) ( pt) show measurements in equation Vbox = x6.3 m 3 x (3 pt) ( pt) Showing through every step 1 pt Final answer is numerically correct. 1 pt Final answer has correct sigdigs. 1 pt Units of answer matches work. Page 6 of 10

7 Question A sphere has a radius of cm. Follow the instructions below to calculate the volume of the sphere. a) What is the radius of the sphere? If you need to calculate it, use the space below to write the equation for the radius of the sphere, and then plug-n-chug. (1 pt all or nothing) Answer for Question a r = cm (1 pt) 30 s, max: all levels. b) Write the equation for the volume of a sphere in the box provided below (1 pt a/n): (1 pt): You don t have to re-copy the initial eqn. V sphere = ( 4 ) ( ) (r) s. (all levels: this eqn is given) 30 s (Mastery) 1 min 30 s (Competence) c) Using the Equation written in your answer to Question a, calculate the volume of the sphere. (7 pt) min 30 s (mastery) 5 min (competence) V sphere = ( 4 3 ) ( ) (r)3 (0 pt): You don t have to re-copy the initial eqn. V sphere = ( 4 3 ) ( ) ( cm)3 (1 pt): Plug in correct value with correct sigdigs. V sphere = ( 4 3 ) ( ) ( cm 3 ) (1 pt): Hopefully, you will show this step. If you don t show this step and you get the wrong answer you will not receive credit for this point. V sphere = cm 3 ( pt) Work shown through every step. (3 pt): 1 pt Final answer is numerically correct. 1 pt Final answer has correct sigdigs. 1 pt Units of answer matches work. Page 7 of 10

8 Question 3 A sphere has a diameter of cm. Follow the instructions below to calculate the volume of the sphere. 3a) What is the radius of the sphere? If you need to calculate it, use the space below to write the equation for the radius of the sphere, and then plug-n-chug. (6 pt) 30 s (mastery) 1 min (competence) r = d (1 pt) initial radius-diameter equation cm r = ( ) = cm (3 pt) ( pt) units through every step/show work 1 pt Final answer is numerically correct. 1 pt Final answer has correct sigdigs. 1 pt Units of answer matches work. Answer for Question a cm 3b) Write the equation for the volume of a sphere in the box provided below (1 pt a/n): V sphere = ( 4 ) ( ) (r)3 3 3c) Using the Equation written in your answer to Question 3a, calculate the volume of the sphere. (7 pt) min 30 s (mastery) 5 min (competence) V sphere = ( 4 3 ) ( ) (r)3 (0 pt): You don t have to re-copy the initial eqn. V sphere = ( 4 3 ) ( ) (5.000 cm)3 (1 pt): Plug in correct value with correct sigdigs. V sphere = ( 4 3 ) ( ) ( cm 3 ) (1 pt): Hopefully, you will show this step. If you don t show this step and you get the wrong answer you will not receive credit for this point. V sphere = cm 3 ( pt) Work shown through every step. (3 pt): 1 pt Final answer is numerically correct. 1 pt Final answer has correct sigdigs. 1 pt Units of answer matches work. Page 8 of 10

9 Question 4 The volume of a rectangular box is 7.00 dm 3. The length of the box is.4 decimeters. The width of the box is 4.50 dm. Calculate the height (thickness) of the box. 4a) Write the equation for the volume of a box. (1 pt a/n) Vbox = l w h (1 pt) 30 s, max: all levels. 4b) Use the equation for the volume of the box to determine the height (thickness) of the box. You must show your work. (7 pts) NOTE: SHOWING YOUR WORK. Rearrange Equation Before Plugging in Values Plug-n-Chug Values/Simplify-As-You-Go Vbox = l w h Rewrite initial equation 1 PT Rewrite initial equation Vbox = l w h V box l w = l w h l w Solve for height Plug in all known values V box PT l w = h Combine like terms before dividing dm 3 = (.4 dm) (4.50 dm) h 7.00 dm 3 = 10.8 dm h 7.00 dm 3 (.4 dm) (4.50 dm) = h Plug in known values Isolate height 7.00 dm dm h = 10.8 dm 10.8 dm x.5 dmx = h Simplify. Final answer must be numerically correct, have the correct number of sigdigs. The units in the answer must match the units in your work. 3 PT Simplify. Final answer must be numerically correct, have the correct number of sigdigs. The units in the answer must match the units in your work. x.5 dmx = h Units through each step 1 min 30 s (mastery) 3 min (competence) 1 PT Units through each step 1 min 30 s (mastery) 3 min (competence) Page 9 of 10

10 Question 5 The volume of a rectangular box is 450. cm 3. The height of the box is.50 cm. Calculate the area of the box. 5a) Write the equation for the volume of a box. (1 pt all or nothing) Vbox = l w h (1 pt a/n) 30 s, max: all levels. 5b) Rewrite the volume equation from Question 5a so that area is represented. ( pt a/n) Vbox = A h ( pt a/n) 30 s, max: all levels. Note: It is your responsibility to remember that area = length width 5c) Use the equation for the volume of the box to determine the area of the box. You must show your work. (7 pts) Note: Showing Work: From now on, I will show the Plug-n-Chug Values First/Simplify-As-You-Go Method. Those of you who are comfortable rearranging equations will still be able to compare your answers. Plug-n-Chug Values/Simplify-As-You-Go 1 PT Rewrite initial equation Vbox = A h Plug in all known values cm 3 = A (.50 cm) PT Isolate area cm 3.50 cm = A (.50 cm).50 cm 3 PT Simplify. Final answer must be numerically correct, have the correct number of sigdigs. The units in the answer must match the units in your work. x180. cm x = A 1 PT Units through each step 1 min 30 s (mastery) 3 min (competence) Page 10 of 10

REVIEW PACKET FOR CHEM 110 EXAM 1

REVIEW PACKET FOR CHEM 110 EXAM 1 EXAM FORMAT You will have one hour for the exam. Expert Level (A+): Finished at 30 min Mastery Level (A): Finished between 30 min and 45 min Proficiency Level (B): Finished