Calculate the value of the cylinder (V) using the formula V = π/4(D² - d²) P cm³, where D is the external diameter, d is the internal diameter, and P is the depth.

Steps to Solve

1. Understand the Formula
   The volume ( V ) of a cylindrical shell is given by the formula:
   $$ V = \frac{\pi}{4} (D^2 - d^2) P $$
   where ( D ) is the external diameter, ( d ) is the internal diameter, and ( P ) is the depth.

2. Identify Values
   From the question, identify the values of ( D ), ( d ), and ( P ). In this case, you have ( D = 2 ), ( d = 1 ), and ( P = 4 ) (assuming these are in centimeters, as indicated by cm³).

3. Plug in the Values
   Substitute the values into the volume formula:
   $$ V = \frac{\pi}{4} (2^2 - 1^2) \cdot 4 $$

4. Calculate the Squares
   Calculate ( D^2 ) and ( d^2 ):
   $$ D^2 = 2^2 = 4 $$
   $$ d^2 = 1^2 = 1 $$

5. Subtract the Squares
   Now substitute these values back into the formula:
   $$ V = \frac{\pi}{4} (4 - 1) \cdot 4 $$

6. Simplify
   Continue simplifying:
   $$ V = \frac{\pi}{4} (3) \cdot 4 $$
   $$ V = 3\pi $$

7. Final Calculation
   The final volume can be approximated as:
   $$ V \approx 3 \times 3.14 = 9.42 \text{ cm}^3 $$