A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be `345\ c m^3`. Check whether she is correct, taking the above as the inside measuremets.

Explanation

To determine whether the child's measurement of the volume of the spherical glass vessel is correct, we will calculate the volume of the vessel by finding the volume of both the spherical part and the cylindrical neck.

### Step-by-Step Solution:

1. **Identify the dimensions:**
- The diameter of the spherical part is 8.5 cm, so the radius \( r_s \) of the sphere is:
\[
r_s = \frac{8.5}{2} = 4.25 \text{ cm}
...