A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is `tan^(-1)(0. 5)`. Water is poured into it at a constant rate of 5 cubic metre per minute. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 10m.

Explanation

To solve the problem step by step, we will follow the given information and derive the required rate at which the water level is rising in the tank.

### Step 1: Understand the shape of the tank
The tank is an inverted right circular cone with a semi-vertical angle given by \( \tan^{-1}(0.5) \). This means that the tangent of the angle \( \theta \) is \( 0.5 \), or \( \tan(\theta) = 0.5 \).

### Step 2: Relate the radius and height
From the definition of the tangent function, we have:
\[
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