Questions: Convert 42.12 cm^3 to cubic inches (in^3) given that 1 inch = 2.54 cm (exact).

Convert 42.12 cm^3 to cubic inches (in^3) given that 1 inch = 2.54 cm (exact).
Transcript text: Convert $42.12 \mathrm{~cm}^{3}$ to cubic inches $\left(\mathrm{in}^{3}\right)$ given that 1 inch $=2.54 \mathrm{~cm}$ (exact).
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Solution

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Solution Steps

To convert cubic centimeters to cubic inches, we need to use the conversion factor between centimeters and inches. Since 1 inch equals 2.54 centimeters, we can cube this conversion factor to convert from cubic centimeters to cubic inches. Specifically, we divide the volume in cubic centimeters by \( (2.54)^3 \) to get the volume in cubic inches.

Step 1: Understand the Conversion Factor

To convert from cubic centimeters to cubic inches, we use the conversion factor between centimeters and inches. Given that \(1 \text{ inch} = 2.54 \text{ cm}\), we need to cube this conversion factor to convert volumes: \[ 1 \text{ in}^3 = (2.54 \text{ cm})^3 \]

Step 2: Calculate the Conversion Factor for Volume

Calculate the conversion factor for cubic centimeters to cubic inches: \[ (2.54)^3 = 16.387064 \]

Step 3: Convert the Volume

Convert the given volume from cubic centimeters to cubic inches using the conversion factor: \[ \text{Volume in in}^3 = \frac{42.12 \text{ cm}^3}{16.387064} \approx 2.570 \]

Final Answer

The volume in cubic inches is \(\boxed{2.570}\).

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