Question

table 1: common conversion factors
length\tvolume\tmass
1 m = 1.0936 yd\t1 l = 1.0567 qt\t1 kg = 2.2046 lb
1 in = 2.54 cm\t1 qt = 0.94635 l\t1 lb = 453.59 g
1 mi = 1.6093 km\t1 ft³ = 28.317 l\t1 oz = 28.349 g
practice
a person has a height of 6.0 ft. what is their height in centimeters?
a person has a height of 65\ ft. what is their height in centimeters?
a sign says your hometown is 286 miles away. what is that distance in kilometers?
a recipe says to use a 2500 ml container; you have a 3 - quart container. is it big enough?
a chunk of gold has a mass of 3.77 lbs. what is its volume in cm³, given its density is 19.32 g/cm³?
what is the volume in liters?

Explanation:

Step1: Convert 6.0 ft to inches

$6.0\ \text{ft} \times 12\ \frac{\text{in}}{\text{ft}} = 72\ \text{in}$

Step2: Convert inches to centimeters

$72\ \text{in} \times 2.54\ \frac{\text{cm}}{\text{in}} = 182.88\ \text{cm}$

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Step1: Convert 6'5" to total inches

$6\ \text{ft} \times 12\ \frac{\text{in}}{\text{ft}} + 5\ \text{in} = 77\ \text{in}$

Step2: Convert inches to centimeters

$77\ \text{in} \times 2.54\ \frac{\text{cm}}{\text{in}} = 195.58\ \text{cm}$

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Step1: Convert miles to kilometers

$286\ \text{mi} \times 1.6093\ \frac{\text{km}}{\text{mi}} = 460.26\ \text{km}$

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Step1: Convert mL to liters

$2500\ \text{mL} = 2.5\ \text{L}$

Step2: Convert quarts to liters

$3\ \text{qt} \times 0.94635\ \frac{\text{L}}{\text{qt}} = 2.839\ \text{L}$

Step3: Compare volumes

$2.839\ \text{L} > 2.5\ \text{L}$

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Step1: Convert lbs to grams

$3.77\ \text{lbs} \times 453.59\ \frac{\text{g}}{\text{lb}} = 1710.03\ \text{g}$

Step2: Calculate volume from density

$\text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{1710.03\ \text{g}}{19.32\ \frac{\text{g}}{\text{cm}^3}} \approx 88.51\ \text{cm}^3$

Step3: Convert $\text{cm}^3$ to liters

$88.51\ \text{cm}^3 = 88.51\ \text{mL} = 0.08851\ \text{L}$

Answer:

1. $182.88\ \text{cm}$
2. $195.58\ \text{cm}$
3. $460.26\ \text{km}$
4. Yes, the 3-quart container is big enough.
5. Volume in $\text{cm}^3$: $88.51\ \text{cm}^3$; Volume in liters: $0.089\ \text{L}$ (rounded to 3 significant figures)