Measurement and Geometry Unit

3.3 Measurement and Dimensional Analysis

  1. Measure the length around your box to the nearest tenth of a centimeter.




  2. Find the area of the base of your box to the nearest tenth.




  3. Find the volume of your box in cubic centimeters. Round to the nearest tenth.




  4. How much dirt would it take to fill your box?




  5. How much ribbon would you need to wrap around your box to add a decorative touch?




  6. How much foil would it take to line the bottom of your box?




  7. Potting soil is sold in cubic feet. How many cubic feet of dirt can your box hold?





  8. If you are driving 70 mph on the interstate, how long will it take you to travel 70 miles?

    9. \(70\;miles\times\frac{1\;hr}{70\;miles}=\;1\;hour\)

  9. One hotel rate in Tokyo is 31,000 yen per night. What is the nightly rate in U.S. dollars? (1 yen=$0.0088)

    10. \(\begin{equation} \frac{31,000 \text { yen }}{1 \text { night }} \times \frac{\$ 0.0088}{1 \text { yen }}=\$ 272.80 \text{ per night} \end{equation} \)

  10. Strawberries in Mexico sell for 28 pesos per kilogram. What is the price in U.S. dollars per pound?

    11. 1 peso = $0.052

    \(\begin{equation} \frac{28 \text { pesos }}{1 \text {kg}} \times \frac{\$ 0.052}{1 \text { peso }} \times \frac{1 \text{ kg}}{2.2 \text{ lbs}}=\$ 0.66 \text{ per pound} \end{equation} \)

  11. The Kentucky Derby race is 10 furlongs. How far is this in
    1. miles?

      \(\begin{equation} \frac{10 \text { furlongs }}{1 \text { race }} \times \frac{0.125 \text{ mi}}{1 \text { furlong }}=1.25 \text{ mi} \end{equation} \)

    2. yards?

      \(\begin{equation} \frac{1.25 \text{ mi}}{1 \text { race }} \times \frac{1760 \text{ yds}}{1 \text{ mi}}=2200 \text{ yds} \end{equation} \)

    3. meters?

      \(\begin{equation} \frac{2200 \text{ yds}}{1 \text { race }} \times \frac{1 \text{ m}}{1.09 \text{ yds}}=2018.3 \text{ m} \end{equation} \)


    12. Use dimensional analysis to solve each problem.

  12. Men’s jeans in Europe have sizes labeled according to waist measurements in centimeters. What size European jeans should a man with a 34 inch waist buy?

    13. \(\begin{equation} \frac{34 \text { in }}{1} \times \frac{2.54 \text { cm }}{1 \text { in }}=86.4 \text { cm} \end{equation} \)

  13. The circumference of the earth is 40,075 km. How many miles is it around the equator?

    14. \(\begin{equation} \frac{40,075 \text { km}}{1 \text { circumference }} \times \frac{1 \text { mi}}{1.61 \text{ km}}=24,891.3 \text { mi} \end{equation} \)

  14. How many miles is a 5K (5 km) road race?

    15. \(\begin{equation} \frac{5 \text{ km}}{1 \text { race }} \times \frac{1 \text{ mi}}{1.61 \text{ km}}= \text {3.1 mi per race} \end{equation} \)

  15. A roll of dental floss contains 100 yards of floss. If you use 18 inches of floss per day, how many days will the roll last?

    16. \(\begin{equation} \frac{100 \text { yds} }{1 \text { roll }} \times \frac{36 \text { in} }{1 \text { yd} } \times \frac{1 \text { day }}{18 \text { in }}=200 \text { days/roll} \end{equation} \)

  16. A quarter coin is 1.75 mm thick. How many quarters would it take to make a stack 2 inches high?

    17. \(\frac{1\;quarter}{1.75\;mm}\times\frac{10\;mm}{1\;cm}\times\frac{2.54\;cm}{1\;in}\times\frac{2\;in}{1\;stack}=29\;quarters \)

  17. The speed limit on some highways in France is 110 km/hr. What is this speed limit in miles per hour?

    18. \(\begin{equation} \frac{110 \text{ km}}{1 \text{ hr}} \times \frac{1 \text{ mi}}{1.61 \text{ km}}= \text {68 mph} \end{equation} \)

  18. To walk across the continental United States from east to west, you would probably walk about 3000 miles. If your average stride measures 2.2 feet, how many steps would it take you to walk across the country?

    19. \(\begin{equation} \frac{3000 \text{ mi}}{1 \text {trek}} \times \frac{5280 \text{ ft}}{1 \text{ mi}} \times \frac{1 \text { step }}{2.2 \text{ ft}}=7,200,000 \text{ steps per trek} \end{equation} \)

  19. An iPhone 6 measures 5.44 inches in length, whereas an iPhone 6 Plus measures 6.22 inches. How many more millimeters in length is the iPhone 6 Plus?

    20. \(\frac{5.44\;in}{\;1\;iPhone\;6}\times\frac{2.54\;cm}{1\;in}\times\frac{10\;mm}{1\;cm}=\;138.2\;mm\;per\;iPhone\;6 \)

    \(\frac{6.22\;in}{\;1\;iPhone\;6+}\times\frac{2.54\;cm}{1\;in}\times\frac{10\;mm}{1\;cm}=\;158\;mm\;per\;iPhone\;6+\)

    \(\begin{equation} 158-138.2=19.8 \text{ mm difference} \end{equation} \)

  20. You are planning a trip to Venice in December. The average high temperature for that time of year is 7 degrees Celsius. What Fahrenheit temperature is this?

    21. \(\begin{equation} F=\frac{9}{5}(7)+32=44.6^{\circ} \mathrm{F} \end{equation} \)

  21. You are making homemade candy. The recipe says to boil the candy mixture until it reaches 250 degrees Fahrenheit. However, your candy thermometer only shows Celsius. To what temperature should you cook the candy?

    22. \(\begin{equation} C=\frac{5}{9}(250-32)=121.1^{\circ} \mathrm{C} \end{equation} \)

  22. A wooden bridge over a small creek on a mountain road has a 1 ton limit. Your Honda Civic manual says your car weighs 1179 kg. Can you safely drive across the bridge? How do you know?

    23. \(\begin{equation} \frac{1 \text { Ton }}{2000 \text{ lbs}} \times \frac{2.2 \text{ lbs}}{1 \text{ kg}} \times \frac{1179 \text{ kg}}{1 \text { Civic }}=1.3 \text{ Tons per Civic} \end{equation} \)

    No, the car is too heavy to be driven over the bridge.

  23. What is the gasoline capacity in liters for a car that holds 13 gallons?

    24. \(\begin{equation} \frac{13 \text{ gal}}{1 \text{ tank}} \times \frac{1 \text{ L}}{0.2642 \text{ gal}}=49 \text{ Liters per tank} \end{equation} \)

  24. Convert 3598 grams into pounds

    25. \(\begin{equation} \frac{3598 \text{ g}}{1} \times \frac{1 \text{ kg}}{1000 \text{ g} }\times \frac{2.2 \text { lbs}}{1 \text{ kg}}=7.9156 \text{ lbs} \end{equation} \)

  25. Convert 231 grams into ounces.

    26. \(\begin{equation} \frac{231 \text{ g}}{1} \times \frac{1 \text { kg}}{1000 \text{ g}} \times \frac{2.2 \text{ lbs}}{1 \text{ kg}} \times \frac{16 \text{ oz}}{1 \text{ lb}}=8.1312 \text{ oz} \end{equation} \)

  26. A beaker contains 578 mL of water. What is the volume in quarts?

    27. \(\begin{equation} \frac{578 \text{ ml}}{1} \times \frac{1 \text{ L}}{1000 \text{ ml}} \times \frac{0.2642 \text{ gal}}{1 \text{ L}} \times \frac{4 \text{ qts}}{1 \text{ gal}}=0.6108 \text{ qts} \end{equation} \)

  27. What is 7.86 kL in L?

    28. \(7.86\;kL\times\frac{1000\;L}{1\;kL}=7860\;L \)

  28. What is 0.0032 gallons in mL?

    29. \(\begin{equation} \frac{0.0032 \text { gal}}{1} \times \frac{1 \text{ L}}{0.2642 \text{ gal}} \times \frac{1000 \text{ ml}}{1 \text{ L}}=12.112 \text{ ml} \end{equation} \)

  29. A box measures 3.12 ft in length, 0.0455 yd in width and 7.87 inches in height. What is its volume in cubic centimeters?

    30. \(3.12\;ft\times\frac{12\;in}{1\;ft}=37.44\;in\)

    \(0.0455\;yd\times\frac{36\;in}{1\;yd}=1.638\;in\)

    \(V=lwh\)

    \(V=(37.44)(1.638)(7.87)\)

    \(482.64\;in^3\times\frac{2.54^3\;cm^3}{1^3\;in^3}=7909.05\;cm^3\)

  30. A block occupies 0.2587 cubic feet. What is its volume in cubic centimeters?

    31. \(\begin{equation} \frac{0.2587 \text{ ft}^{3}} {1} \times \frac{12^{3} { \text{ in}^{3}}}{1^{3} \text{ ft}^{3}} \times \frac{2.54^{3} \text{ cm}^{3}}{1^{3} \text{ in}^{3}} =7325.57 { \text{ cm}^{3}} \end{equation} \)

  31. If you are going 55 mph, what is your speed in meters per second?

    32. \(\begin{equation} \frac{55 \text{ mi}}{1 \text{ hr}} \times \frac{1.61 \text{ km}}{1 \text{ mi}} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ hr}}{60 \text{ min}} \times \frac{1 \text{ min}}{60 \text{ sec}}=24.6 \text{ m/sec} \end{equation} \)

  32. If the density of an object is 2.87 lbs/cubic inch, what is its density in g/mL?

    33. \(\begin{equation} \frac{2.87 \text{ lbs}}{1 \text{ in}^{3}} \times \frac{1 \text{ kg}}{2.2 \text{ lbs}} \times \frac{1000 \text{ g}}{1 \text{ kg}} \times \frac{12^{3} \text{ in}^{3}}{1^{3} \text{ ft}^{3}} \times \frac{1^{3} \text{ ft}^{3}}{7.48 \text{ gal}} \times \frac{0.2642 \text{ gal}}{1\text{ L}} \times \frac{1 \text{ L}}{1000 \text{ ml}}=79.62 \text{ g/ml} \end{equation} \)