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Chapter 1: Problem 2

According to the label on a bottle of salad dressing, the volume of the contents is 0.473 liter (L). Using only the conversions \(1 \mathrm{L}=1000 \mathrm{cm}^{3}\) and \(1 \mathrm{in.}=2.54 \mathrm{cm},\) express this volume in cubic inches.

Short Answer

Expert verified
0.473 liters is approximately 28.865 cubic inches.

Step by step solution

01

Convert Liters to Cubic Centimeters

The volume given is 0.473 L. To convert liters to cubic centimeters, use the conversion factor \(1 \mathrm{L} = 1000 \mathrm{cm}^3\). Multiply the volume in liters by this conversion factor: \[0.473 \mathrm{L} \times 1000 \mathrm{cm}^3/\mathrm{L} = 473 \mathrm{cm}^3\] Thus, 0.473 liters is equivalent to 473 cubic centimeters.
02

Convert Cubic Centimeters to Cubic Inches

To convert cubic centimeters to cubic inches, use the conversion factor \(1 \mathrm{in.} = 2.54 \mathrm{cm}\). Therefore, \(1 \mathrm{in.^3} = (2.54 \mathrm{cm})^3\).Calculate:\[1 \mathrm{in.^3} = 2.54 \times 2.54 \times 2.54 \approx 16.387064 \mathrm{cm}^3\]Now, use this cubic conversion to find the volume in cubic inches:\[473 \mathrm{cm}^3 \times \frac{1 \mathrm{in.^3}}{16.387064 \mathrm{cm}^3} \approx 28.865 \mathrm{in.^3}\] Thus, 473 cubic centimeters is approximately 28.865 cubic inches.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cubic Centimeters to Cubic Inches
We often need to convert between different units of measurement, especially when working with volume. One common conversion is from cubic centimeters (cm鲁) to cubic inches (in鲁). This is useful in various fields like cooking, engineering, and everything in between.
To make this conversion, we use the known relationship between centimeters and inches. Since 1 inch equals 2.54 centimeters, a cubic inch is the cube of 2.54 centimeters. This means:
  • 1 in鲁 = (2.54 cm)鲁
  • 1 in鲁 = 16.387064 cm鲁
Remember, we multiply each dimension by 2.54 because we are dealing with volume, not length. In our exercise, this conversion helped us change 473 cm鲁 (found by converting from liters) into 28.865 in鲁.
This step shows how essential it is to understand the basic unit conversions to manage such transformations.
Liter to Cubic Centimeters
Converting liters to cubic centimeters is one of the simpler unit conversions due to the metric system's straightforward nature. In the metric system, everything is based on powers of ten, making it easy to switch between units.
1 liter is equal to 1000 cubic centimeters. So to convert any volume given in liters to cubic centimeters, we simply:
  • Multiply the volume in liters by 1000
For instance, in our exercise, we start with 0.473 liters of salad dressing. By multiplying 0.473 L by 1000, we get 473 cm鲁.
This step just translates liters into a form (cubic centimeters) better suited for further conversions or usage in equations needing smaller unit measurements. The simplicity here lies in multiplication by a neat round figure of 1000.
Measurement Conversion
Measurement conversion is the process of changing a quantity from one unit to another. It is crucial in science, cooking, construction, or any field where accurate measurements are essential.
Each unit conversion involves a conversion factor 鈥� a number used to multiply or divide the original measurement to get to the target unit. In our example, two conversion factors were applied:
  • Converting from liters to cubic centimeters using 1000 (as 1 L = 1000 cm鲁)
  • Moving from cubic centimeters to cubic inches with approximately 16.387064 (since 1 in鲁 = 16.387064 cm鲁)
Simple arithmetic, like multiplication and division, is generally used with these conversion factors. Always ensure units are consistent for accurate calculations.
Measurement conversion is about understanding how different systems and units relate, allowing one to transition seamlessly between them. This knowledge is especially powerful across countries using different measurement systems or when precise engineering or scientific calculations are necessary.

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Most popular questions from this chapter

A spelunker is surveying a cave. She follows a passage 180 \(\mathrm{m}\) straight west, then 210 \(\mathrm{m}\) in a direction \(45^{\circ}\) east of south, and then 280 \(\mathrm{m}\) at \(30^{\circ}\) east of north. After a fourth unmeasured displacement, she finds herself back where she started. Use a scale drawing to determine the magnitude and direction of the fourth displacement. (See also Problem 1.69 for a different approach to this problem.)

Estimate the number of atoms in your body. (Hint: Based on what you know about biology and chemistry, what are the most common types of atom in your body? What is the mass of each type of atom? Appendix D gives the atomic masses for different elements, measured in atomic mass units; you can find the value of an atomic mass unit, or \(1 \mathrm{u},\) in Appendix E.)

(a) The recommended daily allowance (RDA) of the trace metal magnesium is 410 \(\mathrm{mg} /\) day for males. Express thisquantity in \(\mu \mathrm{g} /\) day. (b) For adults, the RDA of the amino acid lysine is 12 \(\mathrm{mg}\) per \(\mathrm{kg}\) of body weight. How many grams per day should a \(75-\mathrm{kg}\) adult receive? (c) A typical multivitamin tablet can contain 2.0 \(\mathrm{mg}\) of vitamin \(\mathrm{B}_{2}\) (riboflavin), and the RDA is0.0030 \(\mathrm{g} / \mathrm{day}\) . How many such tablets should a person take each day to get the proper amount of this vitamin, assuming that he gets none from any other sources? (d) The RDA for the trace element selenium is 0.000070 \(\mathrm{g} /\) day. Express this dose in mg/day.

A dog in an open field runs 12.0 \(\mathrm{m}\) east and then 28.0 \(\mathrm{m}\) in a direction \(50.0^{\circ}\) west of north. In what direction and how far must the dog then run to end up 10.0 \(\mathrm{m}\) south of her original starting point?

A rocket fires two engines simultaneously. One produces a thrust of 480 \(\mathrm{N}\) directly forward, while the other gives a \(513-\mathrm{N}\) thrust at \(32.4^{\circ}\) above the forward direction. Find the magnitude and direction (relative to the forward direction) of the resultant force that these engines exert on the rocket.
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