Math Problem Statement

1.) How many inches are in 1.00 km?

1π‘˜π‘š Γ— 1000π‘š/1π‘˜π‘š Γ— 100π‘π‘š/1π‘š Γ— 1π‘–π‘›π‘β„Ž/2.54𝑐

2.) If the density of carbon tetrachloride is 0.793 g/mL, and a sample has a volume of 9.29 mL, what is the mass?

9.29 π‘šπΏ Γ— 0.793 𝑔/1 π‘šπΏ

3.) 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?

4.) Example #4 A block occupies 0.2587 cubic ft. What is its volume in cubic mm?

Solution

Let's solve each of these problems step by step.

1. How many inches are in 1.00 km?

We can solve this by converting kilometers to meters, meters to centimeters, and finally centimeters to inches.

1 kmΓ—1000 m1 kmΓ—100 cm1 mΓ—1 inch2.54 cm1 \text{ km} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{100 \text{ cm}}{1 \text{ m}} \times \frac{1 \text{ inch}}{2.54 \text{ cm}}

= \frac{100,000}{2.54} \text{ inches}$$ $$= 39,370.08 \text{ inches}$$ So, there are **39,370.08 inches** in 1.00 km. ### 2. If the density of carbon tetrachloride is 0.793 g/mL, and a sample has a volume of 9.29 mL, what is the mass? The mass can be calculated using the formula: $$\text{Mass} = \text{Density} \times \text{Volume}$$ $$\text{Mass} = 9.29 \text{ mL} \times 0.793 \text{ g/mL} = 7.36797 \text{ g}$$ So, the mass of the sample is **7.37 g** (rounded to two decimal places). ### 3. A box measures 3.12 ft in length, 0.0455 yd in width, and 7.87 inches in height. What is its volume in cubic centimeters? First, convert all measurements to centimeters: - 1 ft = 30.48 cm, so 3.12 ft = $$3.12 \times 30.48 = 95.0976$$ cm. - 1 yd = 91.44 cm, so 0.0455 yd = $$0.0455 \times 91.44 = 4.15932$$ cm. - 1 inch = 2.54 cm, so 7.87 inches = $$7.87 \times 2.54 = 19.9898$$ cm. Now, calculate the volume: $$\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$$ $$\text{Volume} = 95.0976 \text{ cm} \times 4.15932 \text{ cm} \times 19.9898 \text{ cm} = 7915.56 \text{ cubic centimeters}$$ So, the volume of the box is **7915.56 cubic centimeters**. ### 4. A block occupies 0.2587 cubic ft. What is its volume in cubic mm? First, convert cubic feet to cubic inches: - 1 ft = 12 inches, so 1 cubic ft = $$12^3 = 1728$$ cubic inches. $$0.2587 \text{ cubic ft} = 0.2587 \times 1728 \text{ cubic inches} = 447.4416 \text{ cubic inches}$$ Next, convert cubic inches to cubic centimeters: - 1 inch = 2.54 cm, so 1 cubic inch = $$2.54^3 = 16.387064$$ cubic cm. $$447.4416 \text{ cubic inches} = 447.4416 \times 16.387064 \text{ cubic cm} = 7335.22 \text{ cubic centimeters}$$ Finally, convert cubic centimeters to cubic millimeters: - 1 cm = 10 mm, so 1 cubic cm = $$10^3 = 1000$$ cubic mm. $$7335.22 \text{ cubic centimeters} = 7335.22 \times 1000 \text{ cubic mm} = 7335220 \text{ cubic mm}$$ So, the volume of the block is **7,335,220 cubic millimeters**. --- Would you like more details on any of these calculations or have any other questions? ### Related Questions: 1. How do you convert inches to kilometers? 2. What is the process for converting between volume units in different measurement systems? 3. What are the common density units used in chemistry? 4. How would you convert cubic inches to cubic meters? 5. Can you explain why 1 inch is equivalent to 2.54 cm? 6. How does changing the dimensions of a box affect its volume? 7. What is the significance of significant figures in these calculations? 8. What are the key differences between metric and imperial units in volume calculations? ### Tip: When converting units, always ensure you multiply by conversion factors that are fractions equal to 1, such as $$\frac{100 \text{ cm}}{1 \text{ m}}$$, to avoid changing the value during conversion.

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Volume Calculations
Density Calculations

Formulas

Density = Mass / Volume
Volume = Length Γ— Width Γ— Height

Theorems

-

Suitable Grade Level

High School

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