Water is filled in a closed cylindrical vessel of 10 cm height and base radius `sqrt(10//pi)` cm. The open ends ofthe cylinder are closed by two metal discs made ofa material whose thickness is `10^(-3)m` and having thermal conductivity `200W//m^(@)C.` If water temperature inside the cylinder is `50^(@)C` and surrounding temperature is `20^(@)C,` findthe time taken for the temperature to fall by `1^(@)C,` Given that the specific heat ofwater is `4200J//kg^(@)C.` and heat loss from water only takes place by the discs as the walls are made up of a thermally insulating material.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the area of the metal discs
The area \( A \) of the circular base of the cylinder can be calculated using the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the base. Given that the radius \( r = \sqrt{\frac{10}{\pi}} \) cm, we first convert it to meters:
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