A spherical iron ball of radius 10cm, coated with a layer of ice of uniform thickness, melts at a rate of `100 pi cm^(3) //` min.The rate at which the thickness decreases when the thickness of ice is 5 cm, is

Options

A. `1 cm// ` min
B. `2 cm //`min
C. `(1)/( 376) cm //` min
D. `5 cm //` min

Explanation

To solve the problem step by step, we will follow these procedures:

### Step 1: Understand the problem
We have a spherical iron ball with a radius of 10 cm, coated with a layer of ice of uniform thickness \( x \). The total radius of the sphere with ice is \( r = 10 + x \). The ice melts at a rate of \( \frac{dV}{dt} = -100\pi \) cm³/min (negative because the volume is decreasing).

### Step 2: Write the volume formula
The volume \( V \) of a sphere is given by the formula:
\[
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