1. **Problem statement:** We have two similar statues A and B. The volume of statue B is 20% less than the volume of statue A. We need to find the percentage decrease $k$ in the surface area of statue B compared to statue A. 2. **Key concept:** For similar 3D shapes, the ratio of volumes is the cube of the scale factor $r$, and the ratio of surface areas is the square of the scale factor $r$. 3. **Step 1: Define scale factor $r$:** Let $r$ be the ratio of a linear dimension of statue B to statue A. 4. **Step 2: Use volume relation:** Volume of B = Volume of A $\times r^3$ Given volume of B is 20% less than A, so volume of B = 80% of volume of A. $$r^3 = 0.8$$ 5. **Step 3: Solve for $r$:** $$r = \sqrt[3]{0.8}$$ Calculate: $$r \approx 0.928$$ 6. **Step 4: Find surface area ratio:** Surface area of B = Surface area of A $\times r^2$ $$r^2 = (0.928)^2 = 0.861$$ 7. **Step 5: Calculate percentage decrease $k$ in surface area:** $$k = (1 - r^2) \times 100 = (1 - 0.861) \times 100 = 13.9\%$$ 8. **Final answer:** The surface area of statue B is approximately 13.9% less than that of statue A. **Answer:** $k = 13.9$ (to 3 significant figures)