A metal ball having a diameter of `0.4` m is heated from `273` to `360 K.` If the coefficient of areal expansion of the material of the ball is `0.000034 K^(-1)`, then determine the increase in surface area of the ball.

Explanation

To solve the problem of finding the increase in surface area of a metal ball when it is heated, we can follow these steps:

### Step 1: Determine the radius of the ball
Given the diameter of the ball is \(0.4 \, \text{m}\), we can find the radius \(R\) using the formula:
\[ R = \frac{D}{2} = \frac{0.4 \, \text{m}}{2} = 0.2 \, \text{m} \]

...