1. **Stating the problem:** We have a pyramid (ostrosłup) and a plane parallel to its base that cuts the pyramid into two parts. We need to find the ratio of the volume of the smaller part to the volume of the larger part for the case shown in diagram 4a, where the base is divided into segments 4 and 3. 2. **Key concept:** When a plane cuts a pyramid parallel to its base, the cross-section is similar to the base, and the linear scale factor between the smaller pyramid (top part) and the original pyramid is the ratio of the corresponding edges. 3. **Identify scale factor:** The smaller top pyramid has a base edge length of 3, and the original base edge length is 4 + 3 = 7. So, the linear scale factor is: $$k = \frac{3}{7}$$ 4. **Volume scale factor:** Volumes scale as the cube of the linear scale factor: $$k^3 = \left(\frac{3}{7}\right)^3 = \frac{27}{343}$$ 5. **Volumes of parts:** - Volume of smaller (top) pyramid: $$V_{small} = k^3 V$$ - Volume of larger (bottom) part: $$V_{large} = V - V_{small} = V - k^3 V = V(1 - k^3)$$ 6. **Ratio of volumes:** $$\text{Ratio} = \frac{V_{small}}{V_{large}} = \frac{k^3 V}{V(1 - k^3)} = \frac{k^3}{1 - k^3} = \frac{\frac{27}{343}}{1 - \frac{27}{343}} = \frac{27/343}{316/343} = \frac{27}{316}$$ 7. **Final answer:** The ratio of the volume of the smaller part to the larger part is: $$\boxed{\frac{27}{316}}$$