Question

The most powerful engine available for the classic 1963 Chevrolet Corvette Sting Ray developed 360 horsepower and had a displacement of 327 cubic inches. Express this displacement in liters (L) by using only the conversions 1 L = 1000 cm\(^3\) and 1 in. = 2.54 cm.

Short answer

The displacement is approximately 5.357 liters.

Step-by-step solution

Convert cubic inches to cubic centimeters

First, we need to convert the displacement from cubic inches to cubic centimeters. Since the displacement given is 327 cubic inches, and knowing the conversion factor that 1 inch is equal to 2.54 centimeters, we cube this conversion factor to convert cubic inches to cubic centimeters.Therefore, multiply 327 by \((2.54)^3\) to convert:\[327 \text{ in}^3 \times (2.54 \text{ cm/in})^3 = 327 \times 16.387064 \text{ cm}^3 \approx 5356.669 \text{ cm}^3\]

Convert cubic centimeters to liters

Now, use the conversion factor that 1 liter is equal to 1000 cubic centimeters. To convert 5356.669 cmto liters, divide by 1000:\[\frac{5356.669 \text{ cm}^3}{1000} \approx 5.357 \text{ L}\]

Key concepts

Cubic Inches to Cubic Centimeters

To convert from cubic inches to cubic centimeters, you must first understand how to apply conversion factors correctly. One cubic inch is not the same as a cubic centimeter.
A single inch equals 2.54 centimeters, but here, we are talking about volume—cubic measures—which requires cubing the linear conversion factor.
When you cube a number, you multiply it by itself three times. So, for the conversion factor of inches to centimeters, we use \[ (2.54)^3 = 16.387064 \]. Therefore, each cubic inch is 16.387064 cubic centimeters.
For example, if you have a displacement value of 327 cubic inches, you multiply by this factor: \[327 \times 16.387064 \approx 5356.669 \, \text{cm}^3\]. This gives you the volume in cubic centimeters. With this explanation, you can apply the same principle to other conversions.

Cubic Centimeters to Liters

Cubic centimeters and liters are both units used to measure volume, but they are common in different contexts.
The conversion between these units is straightforward: 1 liter equals 1000 cubic centimeters. This is a linear conversion requiring no complicated calculations.
For the conversion process, if you have a volume in cubic centimeters, such as 5356.669 cm\(^3\), you convert it into liters by dividing the volume by 1000.
This gives: \[ \frac{5356.669}{1000} \approx 5.357 \, \text{L} \]. This results in the volume being expressed in liters, thus making it easier to understand in contexts like automotive engines. Remember that knowing these precise conversions is essential when dealing with scientific or mechanical problems.

Conversion Factors

Conversion factors are numbers or formulas needed to convert one set of units to another. They are crucial in unit conversions.Conversion factors depend on the relationship between the two types of measurements you are using.
For example, if you want to convert inches to centimeters, you use 2.54 cm/in. But if you're converting cubic inches to cubic centimeters, you must use: \[ (2.54)^3 \] because you are dealing with volumes.
Always ensure to cube the factor whenever transitioning between linear and cubic measurements. Also, remember that all kinds of measurements like mass, volume, and length have specific conversion factors.
Properly understanding and utilizing conversion factors ensures calculations are accurate and prevents mistakes in practical applications.

Volume Conversion in Physics

Volume is an essential element in physics when analyzing three-dimensional space. Understanding conversions between different volume units is crucial because it allows scientists and engineers to communicate more effectively.
Knowledge of converting cubic inches to cubic centimeters and then to liters is especially relevant in fields that use both metric and imperial systems.
In physics, the conversion from cubic inches to cubic centimeters involves understanding that volume calculations expand our basic linear conversions into three dimensions.
This conversion is necessary when dealing with many physical applications, like engine displacement, fluid dynamics, or even material science.
Adopting a keen understanding of these conversions is fundamental, as it enables precise measurements and fosters global understanding between disparate scientific fields.