?In purchasing food for a political rally, you erroneously order shucked medium-size

In the United States, a doll house has the scale of 1:12 of a real house (that is, each length of the doll house is \(\frac{1}{12}\) that of the real house) and a miniature house (a doll house to fit within a doll house) has the scale of 1:144 of a real house. Suppose a real house (Fig. 1-7) has a front length of 20 m, a depth of 12 m, a height of 6.0 m, and a standard sloped roof (vertical triangular faces on the ends) of height 3.0 m. In cubic meters, what are the volumes of the corresponding (a) doll house and (b) miniature house? Text Transcription: 1/12

A ton is a measure of volume frequently used in shipping, but that use requires some care because there are at least three types of tons: A displacement ton is equal to 7 barrels bulk, a freight ton is equal to 8 barrels bulk, and a register ton is equal to 20 barrels bulk. A barrel bulk is another measure of volume: 1 barrel bulk = 0.1415 m3 . Suppose you spot a shipping order for “73 tons” of M&M candies, and you are certain that the client who sent the order intended “ton” to refer to volume (instead of weight or mass, as discussed in Chapter 5). If the client actually meant displacement tons, how many extra U.S. bushels of the candies will you erroneously ship if you interpret the order as (a) 73 freight tons and (b) 73 register tons? (\(1 \ \mathrm{m}^{3} = 28.378\) U.S. bushels.) Text Transcription: 1 m^3=28.378

Two types of barrel units were in use in the 1920s in the United States. The apple barrel had a legally set volume of 7056 cubic inches; the cranberry barrel, 5826 cubic inches. If a merchant sells 20 cranberry barrels of goods to a customer who thinks he is receiving apple barrels, what is the discrepancy in the shipment volume in liters?

An old English children’s rhyme states, “Little Miss Muffet sat on a tuffet, eating her curds and whey, when along came a spider who sat down beside her. . . .” The spider sat down not because of the curds and whey but because Miss Muffet had a stash of 11 tuffets of dried flies. The volume measure of a tuffet is given by 1 tuffet = 2 pecks = 0.50 Imperial bushel, where 1 Imperial bushel = 36.3687 liters (L). What was Miss Muffet’s stash in (a) pecks, (b) Imperial bushels, and (c) liters?

Table 1-7 shows some old measures of liquid volume. To complete the table, what numbers (to three significant figures) should be entered in (a) the wey column, (b) the chaldron column, (c) the bag column, (d) the pottle column, and (e) the gill column, starting from the top down? (f) The volume of 1 bag is equal to \(0.1091 \ \mathrm{m}^{3}\) . If an old story has a witch cooking up some vile liquid in a cauldron of volume 1.5 chaldrons, what is the volume in cubic meters? Text Transcription: 0.1091 m^3

A typical sugar cube has an edge length of 1 cm. If you had a cubical box that contained a mole of sugar cubes, what would its edge length be? (One mole = \(6.02 \times 10^{23}\) units.) Text Transcription: 6.02 times10^23

An old manuscript reveals that a landowner in the time of King Arthur held 3.00 acres of plowed land plus a livestock area of 25.0 perches by 4.00 perches. What was the total area in (a) the old unit of roods and (b) the more modern unit of square meters? Here, 1 acre is an area of 40 perches by 4 perches, 1 rood is an area of 40 perches by 1 perch, and 1 perch is the length 16.5 ft.

A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car’s fuel consumption was at the rate of 40 miles per gallon on the open road. The tourist does not realize that the U.K. gallon differs from the U.S. gallon: 1 U.K. gallon = 4.546 090 0 liters 1 U.S. gallon = 3.785 411 8 liters. For a trip of 750 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?

Using conversions and data in the chapter, determine the number of hydrogen atoms required to obtain 1.0 kg of hydrogen. A hydrogen atom has a mass of 1.0 u.

A cord is a volume of cut wood equal to a stack 8 ft long, 4 ft wide, and 4 ft high. How many cords are in \(1.0 \mathrm{~m}^{3}\) ? Text Transcription: 1.0 m^3

One molecule of water \(\left(\mathrm{H}_{2} \mathrm{O}\right)\) contains two atoms of hydrogen and one atom of oxygen. A hydrogen atom has a mass of 1.0 u and an atom of oxygen has a mass of 16 u, approximately. (a) What is the mass in kilograms of one molecule of water? (b) How many molecules of water are in the world’s oceans, which have an estimated total mass of \(1.4 \times 10^{21} \mathrm{~kg}\)? Text Transcription: H2O 1.4 times 10^21 kg

A person on a diet might lose 2.3 kg per week. Express the mass loss rate in milligrams per second, as if the dieter could sense the second-by-second loss.

What mass of water fell on the town in Problem 7? Water has a density of \(1.0 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\). Text Transcription: 1.0 times 10^3 kg/m^3

(a) A unit of time sometimes used in microscopic physics is the shake. One shake equals \(10^{-8}\) s. Are there more shakes in a second than there are seconds in a year? (b) Humans have existed for about \(10^{6}\) years, whereas the universe is about \(10^{10}\) years old. If the age of the universe is defined as 1 “universe day,” where a universe day consists of “universe seconds” as a normal day consists of normal seconds, how many universe seconds have humans existed? Text Transcription: 10^-8 10^6 10^10

A unit of area often used in measuring land areas is the hectare, defined as \(10^{4} \mathrm{~m}^{2}\) . An open-pit coal mine consumes 75 hectares of land, down to a depth of 26 m, each year. What volume of earth, in cubic kilometers, is removed in this time? Text Transcription: 10^4 m^2

An astronomical unit (AU) is the average distance between Earth and the Sun, approximately \(1.50 \times 10^{8} \mathrm{~km}\). The speed of light is about \(3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}\). Express the speed of light in astronomical units per minute. Text Transcription: 1.50 times 10^8 km 3.0 times 10^8 m/s

The common Eastern mole, a mammal, typically has a mass of 75 g, which corresponds to about 7.5 moles of atoms. (A mole of atoms is \(6.02 \times 10^{23}\) atoms.) In atomic mass units (u), what is the average mass of the atoms in the common Eastern mole? Text Transcription: 6.02 times 10^23

A traditional unit of length in Japan is the ken (1 ken = 1.97 m). What are the ratios of (a) square kens to square meters and (b) cubic kens to cubic meters? What is the volume of a cylindrical water tank of height 5.50 kens and radius 3.00 kens in (c) cubic kens and (d) cubic meters?

You receive orders to sail due east for 24.5 mi to put your salvage ship directly over a sunken pirate ship. However, when your divers probe the ocean floor at that location and find no evidence of a ship, you radio back to your source of information, only to discover that the sailing distance was supposed to be 24.5 nautical miles, not regular miles. Use the Length table in Appendix D to calculate how far horizontally you are from the pirate ship in kilometers.

The cubit is an ancient unit of length based on the distance between the elbow and the tip of the middle finger of the measurer. Assume that the distance ranged from 43 to 53 cm, and suppose that ancient drawings indicate that a cylindrical pillar was to have a length of 9 cubits and a diameter of 2 cubits. For the stated range, what are the lower value and the upper value, respectively, for (a) the cylinder’s length in meters, (b) the cylinder’s length in millimeters, and (c) the cylinder’s volume in cubic meters?

As a contrast between the old and the modern and between the large and the small, consider the following: In old rural England 1 hide (between 100 and 120 acres) was the area of land needed to sustain one family with a single plough for one year. (An area of 1 acre is equal to \(4047 \ \mathrm{~m}^{2}\) .) Also, 1 wapentake was the area of land needed by 100 such families. In quantum physics, the cross-sectional area of a nucleus (defined in terms of the chance of a particle hitting and being absorbed by it) is measured in units of barns, where 1 barn is \(1 \times 10^{-28} \mathrm{~m}^{2}\) . (In nuclear physics jargon, if a nucleus is “large,” then shooting a particle at it is like shooting a bullet at a barn door, which can hardly be missed.) What is the ratio of 25 wapentakes to 11 barns? Text Transcription: 4047 m^2 1 times 10^-28 m^2

An astronomical unit (AU) is equal to the average distance from Earth to the Sun, about \(92.9 \times 10^{6} \mathrm{mi}\) mi. A parsec (pc) is the distance at which a length of 1 AU would subtend an angle of exactly 1 second of arc (Fig. 1-8). A light-year (ly) is the distance that light, traveling through a vacuum with a speed of 186 000 mi/s, would cover in 1.0 year. Express the Earth–Sun distance in (a) parsecs and (b) light-years. Text Transcription: 92.9 times 10^6 mi

The description for a certain brand of house paint claims a coverage of \(460 \ \mathrm{ft}^{2} / \mathrm{gal}\). (a) Express this quantity in square meters per liter. (b) Express this quantity in an SI unit (see Appendices A and D). (c) What is the inverse of the original quantity, and (d) what is its physical significance? Text Transcription: 460 ft^2 gal

Strangely, the wine for a large wedding reception is to be served in a stunning cut-glass receptacle with the interior dimensions of \(40 \mathrm{~cm} \times 40 \mathrm{~cm} \times 30 \mathrm{~cm}\) (height). The receptacle is to be initially filled to the top. The wine can be purchased in bottles of the sizes given in the following table. Purchasing a larger bottle instead of multiple smaller bottles decreases the overall cost of the wine. To minimize the cost, (a) which bottle sizes should be purchased and how many of each should be purchased and, once the receptacle is filled, how much wine is left over in terms of (b) standard bottles and (c) liters? 1 standard bottle 1 magnum = 2 standard bottles 1 jeroboam = 4 standard bottles 1 rehoboam = 6 standard bottles 1 methuselah = 8 standard bottles 1 salmanazar = 12 standard bottles 1 balthazar = 16 standard bottles = 11.356 L 1 nebuchadnezzar = 20 standard bottles Text Transcription: 40 cm times 40 cm times 30 cm

The corn–hog ratio is a financial term used in the pig market and presumably is related to the cost of feeding a pig until it is large enough for market. It is defined as the ratio of the market price of a pig with a mass of 3.108 slugs to the market price of a U.S. bushel of corn. (The word “slug” is derived from an old German word that means “to hit”; we have the same meaning for “slug” as a verb in modern English.) A U.S. bushel is equal to 35.238 L. If the corn–hog ratio is listed as 5.7 on the market exchange, what is it in the metric units of \(\frac{\text { price of } 1 \text { kilogram of pig }}{\text { price of } 1 \text { liter of corn }} \text { ? }\) (Hint: See the Mass table in Appendix D.) Text Transcription: price of 1 kilogram of pig / price of 1 liter of corn

You are to fix dinners for 400 people at a convention of Mexican food fans. Your recipe calls for 2 jalapeño peppers per serving (one serving per person). However, you have only habanero peppers on hand. The spiciness of peppers is measured in terms of the scoville heat unit (SHU). On average, one jalapeño pepper has a spiciness of 4000 SHU and one habanero pepper has a spiciness of 300 000 SHU. To get the desired spiciness, how many habanero peppers should you substitute for the jalapeño peppers in the recipe for the 400 dinners?

A standard interior staircase has steps each with a rise (height) of 19 cm and a run (horizontal depth) of 23 cm. Research suggests that the stairs would be safer for descent if the run were, instead, 28 cm. For a particular staircase of total height 4.57 m, how much farther into the room would the staircase extend if this change in run were made?

In purchasing food for a political rally, you erroneously order shucked medium-size Pacific oysters (which come 8 to 12 per U.S. pint) instead of shucked medium-size Atlantic oysters (which come \(1.0 \mathrm{~m} \mathrm{} \times 12 \mathrm{~cm} \times 20 \mathrm{~cm}\), and a U.S. pint is equivalent to 0.4732 liter. By how many oysters is the order short of your anticipated count? Text Transcription: 1.0 m times 12 cm times 20 cm

An old English cookbook carries this recipe for cream of nettle soup: “Boil stock of the following amount: 1 breakfastcup plus 1 teacup plus 6 tablespoons plus 1 dessertspoon. Using gloves, separate nettle tops until you have 0.5 quart; add the tops to the boiling stock. Add 1 tablespoon of cooked rice and 1 saltspoon of salt. Simmer for 15 min.” The following table gives some of the conversions among old (premetric) British measures and among common (still premetric) U.S. measures. (These measures just scream for metrication.) For liquid measures, 1 British teaspoon = 1 U.S. teaspoon. For dry measures, 1 British teaspoon = 2 U.S. teaspoons and 1 British quart = 1 U.S. quart. In U.S. measures, how much (a) stock, (b) nettle tops, (c) rice, and (d) salt are required in the recipe?