To find the diameter of the cylinder, we need to first find the radius using the formula for the volume of a cylinder.
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given that the volume is 29,673 inches^3, the height is 42 cm (which we need to convert to inches), and π = 3.14, we can substitute these values into the formula to solve for the radius.
29,673 = 3.14r^2 * 42
r^2 = 29,673 / (3.14 * 42)
r^2 = 223.69
r = √223.69
r = 14.95 inches
Now that we have found the radius, we can find the diameter by multiplying the radius by 2.
Diameter = 2 * radius
Diameter = 2 * 14.95
Diameter = 29.9 inches
Therefore, the diameter of the cylinder is 29.9 inches.