estions A laboratory experiment requires 7.00 g of aluminum wire (d=2.70g/cm^3) The diameter of the wire is 0.200 in. Determine the length of the wire, in centimeters to be used for this experiment. The volume of a cylinder is pi r^2e where r=radius and l=length. square cm

To determine the length of the aluminum wire, we need to use the formula for the volume of a cylinder:<br /><br />\[ V = \pi r^2 h \]<br /><br />where:<br />- \( V \) is the volume of the cylinder,<br />- \( r \) is the radius of the cylinder,<br />- \( h \) is the height (or length) of the cylinder.<br /><br />Given:<br />- The mass of the aluminum wire is \( 7.00 \) grams.<br />- The density of aluminum is \( 2.70 \) grams per cubic centimeter (\( g/cm^3 \)).<br />- The diameter of the wire is \( 0.200 \) inches.<br /><br />First, we need to convert the diameter from inches to centimeters. Since \( 1 \) inch is equal to \( 2.54 \) centimeters:<br /><br />\[ 0.200 \text{ inches} \times 2.54 \text{ cm/inch} = 0.508 \text{ cm} \]<br /><br />Next, we find the radius by dividing the diameter by 2:<br /><br />\[ r = \frac{0.508 \text{ cm}}{2} = 0.254 \text{ cm} \]<br /><br />Now, we can calculate the volume of the aluminum wire using the density formula:<br /><br />\[ V = \frac{\text{mass}}{\text{density}} = \frac{7.00 \text{ g}}{2.70 \text{ g/cm}^3} = 2.593 \text{ cm}^3 \]<br /><br />Now that we have the volume, we can solve for the length \( h \) using the volume formula for a cylinder:<br /><br />\[ V = \pi r^2 h \]<br /><br />\[ 2.593 \text{ cm}^3 = \pi (0.254 \text{ cm})^2 h \]<br /><br />\[ 2.593 \text{ cm}^3 = \pi (0.064516 \text{ cm}^2) h \]<br /><br />\[ 2.593 \text{ cm}^3 = 0.203 \text{ cm}^2 \cdot h \]<br /><br />\[ h = \frac{2.593 \text{ cm}^3}{0.203 \text{ cm}^2} \]<br /><br />\[ h \approx 12.83 \text{ cm} \]<br /><br />Therefore, the length of the aluminum wire to be used for this experiment is approximately \( 12.83 \) centimeters.