1. **State the problem:** We have two similar cylinders. The smaller cylinder has a volume of 800 cm^3 and a height of 10 cm. The larger cylinder has a height of 15 cm. We need to find the volume of the larger cylinder. 2. **Recall the property of similar shapes:** For similar 3D shapes, the ratio of their volumes is the cube of the ratio of their corresponding linear dimensions. 3. **Set up the ratio of heights:** $$\frac{15}{10} = 1.5$$ 4. **Calculate the volume ratio:** $$\left(1.5\right)^3 = 1.5 \times 1.5 \times 1.5 = 3.375$$ 5. **Find the volume of the larger cylinder:** Multiply the smaller volume by the volume ratio: $$800 \times 3.375 = 2700$$ **Final answer:** The volume of the larger cylinder is **2700 cm^3**.