Practice with Dimensional Analysis

Complete these exercises and check your answers.

Practice - Dimensional Analysis

Use dimensional analysis to convert the following:

1) 7 \, \text{mi}. to yards

2) 234 \, \text{oz}. to tons

3) 11.2 \, \text{mg} to grams

4) 1.35 \, \text{km} to centimeters

5) 9,800,000 \, \text{mm} (milimeters) to miles

6) 4.5 \,\text{ft}^{2} to square yards

7) 435,000 \text{m}^{2} to sqaure kilometers

8) 8 \,\text{km}^{2} to square feet

9) 0.0065 \,\text{km}^{3} to cubic meters

10) 14.62 \, \text{in}^{3} to cubic centimeters

11) 5,500 \, \text{cm}^{3} to cubic yards

12) 3.5 \,\text{mph} (miles per hour) to feet per second

13) 185 \, \text{yd}. per min. to miles per hour

14) 153 \, \text{ft / s} (feet per second) to miles per hour

15) 248 \,\text{mph} to meters per second

16) 186,000 \, \text{mph} to kilometers per year

17) 7.50 \, T / \text{yd}^{2} (tons per square yard) to pounds per square inch

18) 16 \, \text{ft/s}  ^{2} to kilometers per hour squared

Use dimensional analysis to solve the following:

19) On a recent trip, Jan traveled 260 miles using 8 gallons of gas. How many miles per 1-gallon did she travel? How many yards per 1-ounce?

20) A chair lift at the Divide ski resort in Cold Springs, WY is 4806 feet long and takes 9 minutes. What is the average speed in miles per hour? How many feet per second does the lift travel?

21) A certain laser printer can print 12 pages per minute. Determine this printer's output in pages per day, and reams per month. (1 ream =5000 pages)

22) An average human heart beats 60 times per minute. If an average person lives to the age of 75, how many times does the average heart beat in a lifetime?

23) Blood sugar levels are measured in miligrams of gluclose per deciliter of blood volume. If a person's blood sugar level measured 128 mg / dL, how much is this in grams per liter?

24) You are buying carpet to cover a room that measures 38 ft by 40 ft. The carpet cost $18 per square yard. How much will the carpet cost?

25) A car travels 14 miles in 15 minutes. How fast is it going in miles per hour? in meters per second?

26) A cargo container is 50 ft long, 10 ft wide, and 8 ft tall. Find its volume in cubic yards and cubic meters.

27) A local zoning ordinance says that a house's "footprint" (area of its ground floor) cannot occupy more than \frac{1}{4} of the lot it is built on. Suppose you own a \frac{1}{3} acre lot, what is the maximum allowed footprint for your house in square feet? in square inches? \left(1 \, \text{acre} \right. \left.=43560 \text{ft} ^{2}\right)

28) Computer memory is measured in units of bytes, where one byte is enough memory to store one character (a letter in the alphabet or a number). How many typical pages of text can be stored on a 700 -megabyte compact disc?

Assume that one typical page of text contains 2000 characters. (1 megabyte = 1,000,000 bytes)

29) In April 1996, the Department of the Interior released a "spike flood" from the Glen Canyon Dam on the Colorado River. Its purpose was to restore the river and the habitants along its bank. The release from the dam lasted a week at a rate of 25,800 cubic feet of water per second. About how much water was released during the 1 -week flood?

30) The largest single rough diamond ever found, the Cullinan diamond, weighed 3106 carats; how much does the diamond weigh in miligrams? in pounds?

(1 carat - 0.2 grams)

Source: Tyler Wallace,
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