Question

part a how many cubic centimeters are there in 2.11 yd³? express your answer in cubic centimeters to three significant figures. volume = cm³ submit request answer

Explanation:

Step1: Recall the conversion factor for length: 1 yard = 91.44 centimeters.

To convert cubic yards to cubic centimeters, we need to cube the length conversion factor. So, \(1\space\text{yd}^3=(91.44\space\text{cm})^3\).

Step2: Calculate the conversion factor for volume.

First, calculate \(91.44^3\). \(91.44\times91.44 = 8360.2736\), then \(8360.2736\times91.44\approx764554.857984\space\text{cm}^3\) per cubic yard.

Step3: Multiply the given volume in cubic yards by the conversion factor.

We have \(2.11\space\text{yd}^3\). So, the volume in cubic centimeters is \(2.11\times764554.857984\).
Calculate \(2.11\times764554.857984\approx2.11\times7.64554857984\times10^{5}\).
\(2.11\times7.64554857984\approx16.1321075\), then \(16.1321075\times10^{5}=1.61321075\times10^{6}\).

Step4: Round to three significant figures.

The number \(1.61321075\times10^{6}\) rounded to three significant figures is \(1.61\times10^{6}\) (or \(1610000\) when written in standard form).

Answer:

\(1.61\times10^{6}\) (or \(1610000\))