1. Stating the problem: We have a hemispherical bowl with an external radius of 18 cm and a thickness of 3 cm. We need to find the volume of the wood making up the bowl. 2. Define the radii: The external radius is $$R = 18\text{ cm}$$, and the thickness is $$t = 3\text{ cm}$$. Thus, the internal radius is $$r = R - t = 18 - 3 = 15\text{ cm}$$. 3. Recall the formula for the volume of a hemisphere: $$V = \frac{2}{3}\pi r^3$$. 4. Calculate the external volume (volume of the hemisphere with radius 18 cm): $$V_{ext} = \frac{2}{3}\pi (18)^3 = \frac{2}{3}\pi \times 5832 = 3888\pi \text{ cm}^3$$. 5. Calculate the internal volume (volume of the hollow part with radius 15 cm): $$V_{int} = \frac{2}{3}\pi (15)^3 = \frac{2}{3}\pi \times 3375 = 2250\pi \text{ cm}^3$$. 6. The volume of the wood is the difference: $$V_{wood} = V_{ext} - V_{int} = 3888\pi - 2250\pi = 1638\pi \text{ cm}^3$$. 7. Approximate numerical value: $$V_{wood} \approx 1638 \times 3.1416 = 5143.99 \text{ cm}^3$$. Final answer: The volume of the wood in the bowl is approximately $$5144\text{ cm}^3$$.