Final answer:
To find the length of aluminum wire needed, calculate the volume of 12 grams of aluminum using its density, then apply the volume formula for a cylinder with the given diameter. The calculation results in a required wire length of approximately 21.98 cm.
Step-by-step explanation:
To determine the length of the aluminum wire needed for the laboratory experiment, we must first calculate the volume of aluminum that corresponds to twelve grams. We use the density formula, which is mass divided by volume. Given that the density of aluminum is 2.7 g/cm³, and we have 12 grams of it:
Density = mass / volume
2.7 g/cm³ = 12 g / volume
volume = 12 g / 2.7 g/cm³
volume ≈ 4.44 cm³
Using the formula for the volume of a cylinder, V = πr²l, where r is the radius and l is the length, and expressing the diameter in centimeters (0.200 in = 0.508 cm), we can find the radius:
r = diameter / 2
r = 0.508 cm / 2
r ≈ 0.254 cm
Now, substitute the volume and radius into the cylinder volume formula to solve for the length of the wire:
V = πr²l
4.44 cm³ = π(0.254 cm)² * l
l = 4.44 cm³ / (π * 0.254 cm * 0.254 cm)
l ≈ 21.98 cm
Therefore, the length of the aluminum wire needed for the experiment is approximately 21.98 cm.