To find the length of the wire, we need to use the formula for the volume of a cylinder. The formula for the volume of a cylinder is given by V = πr^2h, where V is the volume, r is the radius, and h is the height or length of the cylinder.

Given:
Volume of brass = 2.2 cu dm = 2.2 dm^3
Diameter of wire = 0.50 cm

Step 1: Convert the volume from cubic decimeters (dm^3) to cubic centimeters (cm^3).
1 dm^3 = 1000 cm^3
So, 2.2 dm^3 = 2.2 x 1000 cm^3 = 2200 cm^3

Step 2: Convert the diameter of the wire to radius.
Radius (r) = diameter/2 = 0.50 cm / 2 = 0.25 cm

Step 3: Substitute the values into the formula and solve for the height (h).
V = πr^2h
2200 cm^3 = π(0.25 cm)^2h
2200 cm^3 = π(0.0625 cm^2)h
2200 cm^3 = 0.0625πh
Dividing both sides by 0.0625π, we get:
h = 2200 cm^3 / (0.0625π)

Step 4: Calculate the length of the wire using the formula for the circumference of a circle.
Circumference (C) = 2πr
C = 2π(0.25 cm)
C = 0.5π cm

The length of the wire is equal to the height (h) divided by the circumference (C).
Length = h / C
Length = (2200 cm^3 / (0.0625π)) / (0.5π)
Length = 2200 cm^3 / (0.0625 x 0.5)
Length = 2200 cm^3 / 0.03125
Length ≈ 70400 cm

Therefore, the length of the wire is approximately 70400 cm.