Dimensional Analysis
10. 17 cups = (8.5) pints
11. 18 pounds = (288) oz
12. 7.5 miles = (43650) ft
13. 32 quarts = (8) gal
14. 18 quarts = (72) cups
15. 180,000 inches = (2.84) miles
16. 4.5 tons = (144,000) oz
#12. a mile is 5280 ft, not 5820
The rest look ok (including #15!)
Oops. It would be 39,600, right?
12 is wrong
15 is close. I got 179,942.4 inches
The rest are right.
I'd say #15 is right, since you were given 180,000 inches. 2.84 miles is close enough, IMO.
To solve these dimensional analysis problems, we need to understand the conversion factors between the given units. I will explain how to solve each problem using the given conversions.
10. 17 cups = (8.5) pints
- We know that 1 cup is equal to 0.5 pints (since there are 2 cups in a pint).
- To find the number of pints in 17 cups, we multiply 17 by the conversion factor:
17 cups * 0.5 pints/cup = 8.5 pints
11. 18 pounds = (288) oz
- We know that 1 pound is equal to 16 ounces.
- To find the number of ounces in 18 pounds, we multiply 18 by the conversion factor:
18 pounds * 16 oz/pound = 288 oz
12. 7.5 miles = (43,650) ft
- We know that 1 mile is equal to 5,280 feet.
- To find the number of feet in 7.5 miles, we multiply 7.5 by the conversion factor:
7.5 miles * 5,280 ft/mile = 39,600 ft
13. 32 quarts = (8) gallons
- We know that 1 gallon is equal to 4 quarts.
- To find the number of gallons in 32 quarts, we divide 32 by the conversion factor:
32 quarts / 4 quarts/gallon = 8 gallons
14. 18 quarts = (72) cups
- We know that 1 quart is equal to 4 cups.
- To find the number of cups in 18 quarts, we multiply 18 by the conversion factor:
18 quarts * 4 cups/quart = 72 cups
15. 180,000 inches = (2.84) miles
- We know that 1 mile is equal to 63,360 inches.
- To find the number of miles in 180,000 inches, we divide 180,000 by the conversion factor:
180,000 inches / 63,360 inches/mile = 2.84 miles
16. 4.5 tons = (144,000) ounces
- We know that 1 ton is equal to 32,000 ounces.
- To find the number of ounces in 4.5 tons, we multiply 4.5 by the conversion factor:
4.5 tons * 32,000 oz/ton = 144,000 oz
Using dimensional analysis, we can convert between different units by multiplying or dividing the given quantity by appropriate conversion factors.