Given:
Length of the hollow right circular cylinder (h) = 14 cm
Volume of the metal used in making the cylinder = 176 cm³

To find:
Outer and inner diameter of the cylinder

Solution:
The hollow right circular cylinder can be divided into three parts:
1. Outer curved surface
2. Inner curved surface
3. Two circular bases

Step 1: Find the volume of the cylinder
The volume of the cylinder is given by the formula: V = πr²h
Where V is the volume, r is the radius, and h is the height (length) of the cylinder.

Given that the volume of the metal used in making the cylinder is 176 cm³, we can write the equation as:
176 = πr²h

Step 2: Find the outer and inner curved surface areas
The outer curved surface area is given by the formula: A_outer = 2πrh
The inner curved surface area is given by the formula: A_inner = 2πrh

Step 3: Find the difference between the outer and inner curved surface areas
The difference between the outer and inner curved surface areas is given by the formula: A_diff = A_outer - A_inner

Step 4: Find the outer and inner diameters
The diameter of a circle is twice the radius. Therefore, the outer diameter (D_outer) and inner diameter (D_inner) can be calculated as:
D_outer = 2r_outer
D_inner = 2r_inner

Step 5: Solve the equations
We have three equations:

176 = πr²h
A_outer = 2πr_outerh
A_inner = 2πr_innerh

From the first equation, we can solve for r:
r = √(176 / (πh))

Using this value of r, we can calculate the outer and inner curved surface areas:
A_outer = 2πr_outerh = 2π(√(176 / (πh)))h = 2√(176hπ)
A_inner = 2πr_innerh = 2π(0)h = 0

The difference between the outer and inner curved surface areas is:
A_diff = A_outer - A_inner = 2√(176hπ) - 0 = 2√(176hπ)

Finally, we can find the outer and inner diameters using the formulas we derived earlier:
D_outer = 2r_outer = 2√(176 / (πh))
D_inner = 2r_inner = 2(0) = 0

Conclusion:
The outer diameter of the hollow right circular cylinder is 2√(176 / (πh)) cm, and the inner diameter is 0 cm.