Unit 2A

10a. The area of the floor is 40 yds × 25 yds = 1000 yd². Notice how multiplying two lengths with units of yards gives an area with units of square yards. The volume of the cartons is 40 yds × 25 yds × 3 yds= 3000 yd³. Notice how multiplying three lengths with units of yards gives a volume with units of cubic yards.

12c. Begin with 4 weeks and use conversion factors to convert it to units of minutes. Be sure that the units cancel appropriately:

There are 40,320 minutes in 4 weeks.

14b. The first task is to find the conversion factor for cubic yards to cubic inches. Following the procedure given in class, we begin with the fact that 1 yd = 36 inches. Then we raise both sides of this relation to the third power:

(1 yd)³ = (36 in)³ which implies that 1 yd³ = (36 × 36 × 36) in³ = 46,656 in³.

We see that 1 yd³ = 46,656 in³. We can now use this conversion factor to convert 3 cubic yards to cubic inches:

There are 139,968 cubic inches in 3 cubic yards.

16c. According to the conversion factor in Table 2.1, we see that 1 British pound = $1.51. To convert 75 pounds to dollars, we multiply by the conversion factor in the appropriate form:

We see that 75 British pounds is the same as $113.25.

36. We are given the conversion factor for acres to square feet. Thus, ¼ acre or 0.25 acre is equal to

Thus, the lot has an area of 10,890 square feet. According to the ordinance, a house may occupy at most ¼ of the lot, which is an area of ¼ × 10,890 square feet = 2722.5 ft².

Unit 2B

6a. It’s easiest to relate both a deciliter and a milliliter to a liter. According to Table 2.5, we have 1 liter = 10 deciliters and 1 liter = 1000 milliliters. We see that a deciliter is larger than a milliliter. Furthermore, because 10 deciliters = 1000 milliliters, we know that 1 deciliter is 100 times larger than 1 milliliter.

8b. We need the conversion factor for pounds to kilograms given in Table 2.6: 1 kg = 2.2 lbs. Now we can do the conversion:

There are 68.2 kilograms in 150 pounds.