A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Explanation

To find the inner surface area of the vessel, which consists of a hollow hemisphere mounted on a hollow cylinder, we can follow these steps:

### Step 1: Identify the dimensions
- The diameter of the hemisphere is given as 14 cm.
- Therefore, the radius \( r \) of the hemisphere and the cylinder is:
\[ r = \frac{\text{diameter}}{2} = \frac{14 \, \text{cm}}{2} = 7 \, \text{cm} \]
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