**Step 1 — Find both radii.**
$$R = \text{outer radius} = 6 \text{ cm}, \qquad r = \text{inner radius} = 6 - 1 = 5 \text{ cm}$$

**Step 2 — Write the formula for the volume of the steel (hollow hemisphere).**
$$V = \frac{2}{3}\pi R^3 - \frac{2}{3}\pi r^3 = \frac{2}{3}\pi\left(R^3 - r^3\right)$$

**Step 3 — Substitute the values.**
$$V = \frac{2}{3}\pi\left(6^3 - 5^3\right) = \frac{2}{3}\pi(216 - 125) = \frac{2}{3}\pi(91)$$

**Step 4 — Simplify.**
$$V = \frac{182}{3}\pi \text{ cm}^3$$

**Answer : (B) $\dfrac{182}{3}\pi$**