1. Dimensional Analysis Worksheet
1-25

2. 1. How many inches are there in a football field?

3. 1. How many inches are there in a football field?
(100 yds) ( 3 𝑓𝑡 1 𝑦𝑑 ) ( 12 𝑖𝑛 1 𝑓𝑡 ) = 3600 inches

4. 2. How many feet are there in a mile?

5. 2. How many feet are there in a mile?
5280 feet = 1 mile

6. 3. How many yards are there in a mile?

7. 3. How many yards are there in a mile?
mile = 5280 feet ( 1 𝑦𝑑 3 𝑓𝑡 ) = 1760 yards

8. 4. How many yards are there in a soccer field?

9. 4. How many yards are there in a soccer field?
(100 m) ( 100 𝑐𝑚 1 𝑚 ) ( 1 𝑖𝑛 2.54 𝑐𝑚 ) ( 1 𝑓𝑡 12 𝑖𝑛 ) ( 1 𝑦𝑑 3 𝑓𝑡 ) = yards

10. 5. Ho many paces make up a football field?

11. 5. How many paces make up a football field?

12. 6. How many feet are between the first and second floor of a building?

13. 6. How many feet are between the first and second floor of a building?
( 1 𝑠𝑡𝑜𝑟𝑦 1 ) ( 3 𝑚 1 𝑠𝑡𝑜𝑟𝑦 ) ( 100 𝑐𝑚 1 𝑚 ) ( 2.54 𝑖𝑛 1 𝑐𝑚 ) ( 1 𝑓𝑡 12 𝑖𝑛 ) = 9.84 ft

14. 7. How many seconds are in a year?

15. 7. How many seconds are in a year?
( 1 𝑦𝑒𝑎𝑟 1 ) ( 365 𝑑𝑎𝑦𝑠 1 𝑦𝑒𝑎𝑟 ) ( 24 ℎ𝑟𝑠 1 𝑑𝑎𝑦 ) ( 60 𝑚𝑖𝑛 1 ℎ𝑟 ) ( 60 𝑠𝑒𝑐 1 ℎ𝑟 ) = 3.15 x 107 sec

16. 8. A housefly’s lifespan is 3 days. How many minutes is this?

17. 8. A housefly’s lifespan is 3 days. How many minutes is this?

18. 9. If a person blinks their eyes once every 3 minutes, how many times will they blink in 1 day?

19. ( 24 ℎ𝑜𝑢𝑟𝑠 1 ) ( 60 𝑚𝑖𝑛 1 ℎ𝑟 ) ( 𝑏𝑙𝑖𝑛𝑘𝑠 3 𝑚𝑖𝑛 ) = 480 blinks
9. If a person blinks their eyes once every 3 minutes, how many times will they blink in a day?
( 24 ℎ𝑜𝑢𝑟𝑠 1 ) ( 60 𝑚𝑖𝑛 1 ℎ𝑟 ) ( 𝑏𝑙𝑖𝑛𝑘𝑠 3 𝑚𝑖𝑛 ) = 480 blinks

20. 10. How many grams in a pound?

21. 10. How many grams in a pound?

22. 11. A 1974 car weighs 4000 lbs. How many quarter pound patties is this
11. A 1974 car weighs 4000 lbs. How many quarter pound patties is this? If a Quarter Pounder cost 0.65 in 1974 and the car costs $6000, which is cheaper?

23. 11. A 1974 car weighs 4000 lbs. How many quarter pound patties is this
11. A 1974 car weighs 4000 lbs. How many quarter pound patties is this? If a Quarter Pounder cost 0.65 in 1974 and the car costs $6000, which is cheaper?
( 4000 𝑙𝑏𝑠 1974 𝑐𝑎𝑟 ) ( 𝑞𝑢𝑎𝑟𝑡𝑒𝑟 𝑝𝑜𝑢𝑛𝑑 𝑝𝑎𝑡𝑡𝑦 𝑙𝑏 )
= 16,000 quarter pound patties
( 4000 𝑙𝑏𝑠 1974 𝑐𝑎𝑟 ) ( 𝑄𝑢𝑎𝑟𝑡𝑒𝑟 𝑃𝑜𝑢𝑛𝑑 𝑝𝑎𝑡𝑡𝑦 𝑙𝑏 ) ( 0.65 𝑄𝑢𝑎𝑟𝑡𝑒𝑟 𝑃𝑜𝑢𝑛𝑑 𝑝𝑎𝑡𝑡𝑦 ) = $10,400

24. 12. What is the speed of a car in feet/second that is traveling at 60 mph?

25. ( 60 𝑚𝑝ℎ 1 ℎ𝑟 ) ( 5280 𝑓𝑡 1 𝑚𝑖𝑙𝑒 ) ( 1 ℎ𝑟 3600 𝑠𝑒𝑐 ) = 88.0 ft/sec
12. What is the speed of a car in feet/second that is traveling at 60 mph?
( 60 𝑚𝑝ℎ 1 ℎ𝑟 ) ( 5280 𝑓𝑡 1 𝑚𝑖𝑙𝑒 ) ( 1 ℎ𝑟 3600 𝑠𝑒𝑐 ) = 88.0 ft/sec

26. 13. The space shuttle travels at 28,000 mph while orbiting Earth
13. The space shuttle travels at 28,000 mph while orbiting Earth. How far does it travel in the blink of an eye?

27. 13. The space shuttle travels at 28,000 mph while orbiting Earth
13. The space shuttle travels at 28,000 mph while orbiting Earth. How far does it travel in the blink of an eye?
( 28,000 𝑚𝑖𝑙𝑒𝑠 1 ℎ𝑟 ) ( 1 ℎ𝑟 3600 𝑠𝑒𝑐 ) ( 𝑠𝑒𝑐 1 𝑏𝑙𝑖𝑛𝑘 ) = 0.77 miles/blink

28. 14. A stack of 10 3. 5 inch diskettes is 34 mm high
14. A stack of inch diskettes is 34 mm high. How many diskettes does it take to make a stack 100 yards high?

29. 14. A stack of 10 3. 5 inch diskettes is 34 mm high
14. A stack of inch diskettes is 34 mm high. How many diskettes does it take to make a stack 100 yards high?
( 34 𝑚𝑚 10 𝑑𝑖𝑠𝑘𝑠 ) = ( 3.4 𝑚𝑚 1 𝑑𝑖𝑠𝑘 ) ( 100 𝑦𝑑𝑠 1 ) ( 3 𝑓𝑡 1 𝑦𝑑 ) ( 12 𝑖𝑛 1 𝑓𝑡 ) ( 2.54 𝑐𝑚 1 𝑖𝑛 ) ( 10 𝑚𝑚 1 𝑐𝑚 )( 𝑑𝑖𝑠𝑘 3.5 𝑚𝑚 ) = 26,894 diskettes

30. 15. A physics book is 1.5 inches thick; how many books would it take to make a stack 2 stories high?

31. 15. A physics book is 1.5 inches thick; how many books would it take to make a stack 2 stories high?

32. 16. If you earned a penny every 10 seconds of your life, how much would you have after 65 years?

33. 16. If you earned a penny every 10 seconds of your life, how much would you have after 65 years?
( 65 𝑦𝑒𝑎𝑟𝑠 1 ) ( 365 𝑑𝑎𝑦𝑠 1 𝑦𝑒𝑎𝑟 ) ( 24 ℎ𝑟𝑠 1 𝑑𝑎𝑦 ) ( 3600 𝑠𝑒𝑐 1 ℎ𝑟 ) ( 𝑠𝑒𝑐 ) = $2,049,840

34. 17. A container holds 16 ounces; what is the volume of the container in cubic inches?

35. 17. A container holds 16 ounces; what is the volume of the container in cubic inches?
( 16 oz 1 ) ( 2 liters oz ) ( 1000 𝑚𝐿 1 L ) ( 𝑐𝑚3 𝑚𝐿 ) ( 𝑖𝑛 𝑐𝑚3 ) = 28.9 in3 Volume = pir2h

36. 18. A car traveling at 88 ft/sec. What is the speed in mph?

37. 18. A car traveling at 88 ft/sec. What is the speed in mph?

38. 19. What would 25 mph be in m/s?

39. 19. What would 25 mph be in m/s?
( 25 𝑚𝑖 1 ℎ𝑟 ) ( 1 ℎ𝑜𝑢𝑟 3600 𝑠𝑒𝑐 ) ( 5280 𝑓𝑡 1 𝑚𝑖𝑙𝑒𝑠 ) ( 12 𝑖𝑛 1 𝑓𝑡 ) ( 2.54 𝑐𝑚 1 𝑖𝑛 ) ( 1 𝑚 100 𝑐𝑚 ) = m/s

40. 20. When the space shuttle is at max orbit radius it is traveling 28,000 mph. How many miles/sec is this?

41. ( 28,000 𝑚𝑖𝑙𝑒𝑠 1 ℎ𝑟 ) ( 1 ℎ𝑟 3600 𝑠𝑒𝑐 ) = 7.78 mi/s
20. When the space shuttle is at max orbit radius it is traveling 28,000 mph. How many miles/sec is this?
( 28,000 𝑚𝑖𝑙𝑒𝑠 1 ℎ𝑟 ) ( 1 ℎ𝑟 3600 𝑠𝑒𝑐 ) = 7.78 mi/s

42. 21. A pool holds 20,000 gallons of water
21. A pool holds 20,000 gallons of water. A pond holds 2,000,000 cm3 water. A well holds 12,000 liters. Which holds the most?

43. 21. A pool holds 20,000 gallons of water
21. A pool holds 20,000 gallons of water. A pond holds 2,000,000 cm3 water. A well holds 12,000 liters. Which holds the most?
( 𝑔𝑎𝑙 1 ) ( 128 𝑜𝑧 1 𝑔𝑎𝑙 ) ( 2 𝐿 𝑜𝑧 ) = 79,073 L ( 2,000,000 𝑐𝑚3 1 ) ( 𝑚𝐿 𝑐𝑚3 ) ( 𝐿 1000 𝑚𝐿 ) = 2000 L

44. 22. 2 L of Pepsi costs 0. 99. A gallon of milk costs 1. 89
L of Pepsi costs A gallon of milk costs ounce of Founder’s Choice costs Which is cheapest?

45. 22. 2 L of Pepsi costs 0. 99. A gallon of milk costs 1. 89
L of Pepsi costs A gallon of milk costs ounce of Founder’s Choice costs Which is cheapest?
( 𝐿 ) ( 2 𝐿 𝑜𝑧 ) = oz PEPSI ( 𝑔𝑎𝑙 ) ( 1 𝑔𝑎𝑙 128 𝑜𝑧 ) = oz MILK ( 𝑜𝑧 ) = oz FOUNDER’S CHOICE

46. 23. A fingerprint is about 1.25 in2. How many cm2 is this?

47. 23. A fingerprint is about 1.25 in2. How many cm2 is this?

48. 24. The US covers about 16,000,000 miles2
24. The US covers about 16,000,000 miles2. How many walking paces is this?

49. 24. The US covers about 16,000,000 miles2
24. The US covers about 16,000,000 miles2. How many walking paces is this?
( 16,000,000 1 ) ( 𝑓𝑡2 12 𝑚𝑖𝑙𝑒2 ) ( 122 𝑖𝑛2 12 𝑓𝑡2 ) ( 12 𝑝𝑎𝑐𝑒2 222 𝑖𝑛2 ) = x 1014 paces2