A solid metallic sphere of diameter 20 cm and mass 10 kg is heated to a temperature of `327^@C` and suspended in a box in which a constant temperature of `27^@C` is maintained. Find the rate at which the temperature of the Sphere will fall with time. Stefan's constant`=5.67xx10^-8W//m^(2)//K^(4)` and specific heat of metal `=420J//kg//^(@)C`.

Explanation

To solve the problem of finding the rate at which the temperature of a solid metallic sphere falls when suspended in a constant temperature environment, we can follow these steps:

### Step 1: Calculate the Surface Area of the Sphere
The formula for the surface area \( A \) of a sphere is given by:
\[ A = 4 \pi r^2 \]
Given the diameter of the sphere is 20 cm, we can find the radius \( r \):
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