Water is running into a conical vessel, 15cm deep and 5cm in radius, at the rate of 0.1 `c m^3//s e c` . When the water is 6cm deep, find at what rate it. the water level rising? the water-surface area increasing? the wetted surface of the vessel increasing?

Explanation

Let `{CO}^{prime}={h} O {A}^{prime}={r} {CA}^{prime}=1`



`tan alpha=frac{{OA}}{{CO}}=frac{5}{15}=frac{1}{3} `



`tan alpha=frac{{OA}^{prime}}{{CO}^{prime}}=frac{{r}}{{h}} `



`frac{1}{3}=frac{{r}}{{h}} `



...