1. **Stating the problem:** We have a half-cylinder shape with a bottom diameter of 64 cm, a top diameter of 110 cm, and a total length of 455 cm. It is cut into 4 equal pieces along its length. We need to find the diameters at both edges of each smaller cylinder. 2. **Understanding the shape:** The diameter changes linearly from 64 cm at the bottom to 110 cm at the top over the length of 455 cm. 3. **Formula for linear interpolation:** The diameter $d(x)$ at a distance $x$ from the bottom is given by: $$d(x) = d_{bottom} + \frac{(d_{top} - d_{bottom})}{L} \times x$$ where $d_{bottom} = 64$, $d_{top} = 110$, and $L = 455$ cm. 4. **Calculate the length of each piece:** $$\text{piece length} = \frac{455}{4} = 113.75 \text{ cm}$$ 5. **Calculate diameters at each cut:** - At $x=0$ (bottom edge): $$d(0) = 64 + \frac{110 - 64}{455} \times 0 = 64$$ - At $x=113.75$: $$d(113.75) = 64 + \frac{46}{455} \times 113.75 = 64 + 11.5 = 75.5$$ - At $x=227.5$: $$d(227.5) = 64 + \frac{46}{455} \times 227.5 = 64 + 23 = 87$$ - At $x=341.25$: $$d(341.25) = 64 + \frac{46}{455} \times 341.25 = 64 + 34.5 = 98.5$$ - At $x=455$ (top edge): $$d(455) = 64 + \frac{46}{455} \times 455 = 64 + 46 = 110$$ 6. **Diameters of each piece edges:** - Piece 1: 64 cm to 75.5 cm - Piece 2: 75.5 cm to 87 cm - Piece 3: 87 cm to 98.5 cm - Piece 4: 98.5 cm to 110 cm **Final answer:** The diameters at the edges of the 4 pieces are approximately 64, 75.5, 87, 98.5, and 110 cm respectively.