An inverted cone has a depth of 10cm and a base of radius 5cm. Water is poured into it at the rate of 3/2 c.c. per minute. Find the rate at which the level of water in the cone is rising when the depth is 4cm.

Explanation

To solve the problem step by step, we will follow the mathematical principles of geometry and calculus.

### Step 1: Understand the problem
We have an inverted cone with a height (H) of 10 cm and a base radius (R) of 5 cm. Water is being poured into the cone at a rate of \( \frac{3}{2} \) cc/min. We need to find the rate at which the water level (h) is rising when the depth of the water is 4 cm.

### Step 2: Relate the dimensions of the cone
Since the cone is similar in shape at any height, we can establish a relationship between the radius of the water surface (r) and the height of the water (h). The relationship can be derived from the dimensions of the cone:
\[
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