1. **Problem Statement:** We have a half-open cylinder with length 455 cm, top diameter 110 cm, and bottom diameter 91 cm. The length is divided into 4 equal parts, and we want to find the radius on each part for both the top and bottom sides. 2. **Understanding the problem:** The cylinder's length is divided into 4 equal segments, so each segment length is $\frac{455}{4} = 113.75$ cm. 3. **Radius calculation:** The radius is half the diameter. - Top radius $r_{top} = \frac{110}{2} = 55$ cm - Bottom radius $r_{bottom} = \frac{91}{2} = 45.5$ cm 4. **Radius on each part:** Since the problem implies a linear change in diameter from bottom to top along the length, the radius changes linearly from 45.5 cm to 55 cm over 455 cm. 5. **Formula for radius at position $x$ along the length:** $$r(x) = r_{bottom} + \left(\frac{r_{top} - r_{bottom}}{455}\right) \times x$$ where $x$ is the distance from the bottom. 6. **Calculate radius at each division point:** - At $x=0$ cm (bottom): $r(0) = 45.5$ cm - At $x=113.75$ cm: $r(113.75) = 45.5 + \frac{55 - 45.5}{455} \times 113.75 = 45.5 + \frac{9.5}{455} \times 113.75 = 45.5 + 2.375 = 47.875$ cm - At $x=227.5$ cm: $r(227.5) = 45.5 + \frac{9.5}{455} \times 227.5 = 45.5 + 4.75 = 50.25$ cm - At $x=341.25$ cm: $r(341.25) = 45.5 + \frac{9.5}{455} \times 341.25 = 45.5 + 7.125 = 52.625$ cm - At $x=455$ cm (top): $r(455) = 55$ cm 7. **Summary:** The radius at each quarter length from bottom to top is approximately: - Bottom: 45.5 cm - 1st quarter: 47.875 cm - 2nd quarter: 50.25 cm - 3rd quarter: 52.625 cm - Top: 55 cm These values represent the radius on both sides at each division along the length.