Chapter 1.1, Problem 4EDE

Extended and Discovery Exercise

Exercises 1- 4: Measuring the thickness of a very thin layer of material can be difficult to do directly. For example. it would be difficult to measure the thickness of an oil film on water or a coat of paint with a ruler. However, it can be done indirectly using the following formula.

$Thickness=\frac{Volume}{Area}$

That is, the thickness of a thin layer equals the volume of the substance divided by the area that it covers. For example, if a volume of 1 cubic inch of paint is spread over an area of 100 square inches, then the thickness of the paint equals $\frac{1}{100}$ inch. Use this formula in the following exercises.

1. Thickness of an Oil Film A drop of oil measuring 0.12 cubic centimeter in volume is spilled onto a lake. The oil spreads out in a circular shape having a diameter of 23 centimeters. Approximate the thickness of the oil film.
2. Thickness of Gold Foil A flat, rectangular sheet of gold foil measures 20 centimeters by 30 centimeters and has a mass of 23.16 grams. If 1 cubic centimeter of gold has a mass of 19.3 grams. find the thickness of the gold foil. (Source: U. Haber-Schaim. Introductory Apical Science.)
3. Thickness of Cement A 100-foot-long sidewalk is 5 feet wide. If 125 cubic feet of cement are evenly poured to form the sidewalk, find the thickness of the sidewalk.
4. Depth of a Lake A lake covers 2.5 X 10⁷ square feet and contains 7.5 X 10⁸ cubic feet of water. Find the average depth of the lake.

Classifying Numbers

Exercises 1-6: Classify the number as one or more of the following: natural number, integer, rational number, or real number.

1. $\frac{21}{24}$ (Fraction of people in the United States completing at least 4 years of high school)

2. 695,000 (Number of Facebook status updates every 60 seconds)

3. 7.5 (Average number of gallons of water used each minute while taking a shower)

4. 8.4 (Neilsen rating of the TV show Modern Family the week of January 2, 2012)

5. 90 $\sqrt{2}$ (Distance in feet from home plate to second base on a baseball field)

6. -71 (Wind chill when the temperature is -30°F and the wind speed is 40 mi/hr)

Exercises 7-10: Classify each number as one or more of the following: natural number, integer, rational number, or irrational number.

7. p, -3, $\frac{2}{9}$ , $\sqrt{9}$ , 1. $\bar{3}$ , - $\sqrt{2}$

8. $\frac{3}{1},-\frac{5}{8},\sqrt{7,}$ $0.\overline{45},$ $5.6\times {10}^3$

9. $\sqrt{13},\frac{1}{3},$ $5.1\times {10}^{-6}$ , $-2.33,$ $0.\bar{7},-\sqrt{4}$

10. $-103,\frac{21}{25},\sqrt{100},-\frac{5.7}{10},\frac{2}{9},-1.457,\sqrt{3}$

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