1. **Stating the problem:** We need to find the volume of a cylindrical ring (a hollow cylinder) with outer diameter 30 cm, inner diameter 24 cm, and height 31 cm. 2. **Formula used:** The volume of a cylindrical ring is the difference between the volume of the outer cylinder and the inner cylinder. Volume of a cylinder is given by: $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Calculate the radii:** Outer radius $r_o = \frac{30}{2} = 15$ cm Inner radius $r_i = \frac{24}{2} = 12$ cm 4. **Calculate the volume of the outer cylinder:** $$V_o = \pi r_o^2 h = \pi \times 15^2 \times 31 = \pi \times 225 \times 31$$ 5. **Calculate the volume of the inner cylinder:** $$V_i = \pi r_i^2 h = \pi \times 12^2 \times 31 = \pi \times 144 \times 31$$ 6. **Calculate the volume of the ring:** $$V = V_o - V_i = \pi \times 31 \times (225 - 144) = \pi \times 31 \times 81$$ 7. **Simplify and calculate the numerical value:** $$V = 31 \times 81 \times \pi = 2511 \pi \approx 2511 \times 3.1416 = 7887.5 \text{ cm}^3$$ **Final answer:** The volume of the concrete ring is approximately **7887.5 cm³**.