1. **State the problem:** We need to find the volume of a composite solid made of a cone on top of a cylinder. 2. **Given:** - Cone radius $r = 7$ cm - Cone height $h_{cone} = 18$ cm - Cylinder radius $r = 7$ cm (same as cone) - Cylinder height $h_{cyl} = 5$ cm 3. **Formulas:** - Volume of a cone: $$V_{cone} = \frac{1}{3} \pi r^2 h_{cone}$$ - Volume of a cylinder: $$V_{cyl} = \pi r^2 h_{cyl}$$ 4. **Calculate the volume of the cone:** $$V_{cone} = \frac{1}{3} \pi (7)^2 (18) = \frac{1}{3} \pi \times 49 \times 18$$ 5. Simplify the multiplication inside the cone volume: $$49 \times 18 = 882$$ So, $$V_{cone} = \frac{1}{3} \pi \times 882$$ 6. Simplify the fraction: $$V_{cone} = \pi \times \cancel{\frac{1}{3}} \times 882 = \pi \times 294$$ 7. **Calculate the volume of the cylinder:** $$V_{cyl} = \pi (7)^2 (5) = \pi \times 49 \times 5 = 245 \pi$$ 8. **Total volume of the shape:** $$V_{total} = V_{cone} + V_{cyl} = 294 \pi + 245 \pi = (294 + 245) \pi = 539 \pi$$ **Final answer:** $$\boxed{539 \pi \text{ cm}^3}$$