Question

Water is flowing at the rate of 30 m^3/min from a shallow concrete conical reservoir (vertex down) of base radius 35 m and height 8 m. a. How fast is the water level rising when the water is 3 m deep?

Answer 1

To find the rate at which the water level is rising when the water is 3 m deep in a conical reservoir, we can use similar triangles and the formula for the volume of a cone.

Step-by-step explanation:

To find how fast the water level is rising when the water is 3 m deep, we can use similar triangles and the formula for the volume of a cone.

Let's label the radius of the water surface as r, the height of the water column as h, and the rate at which the water level is rising as dh/dt.

Using similar triangles, we can write the equation: (dh/dt) / (h - 3) = r / (8 - 3)

Next, we can express r in terms of h using the given base radius of 35 m: r = (35/8)h

Substituting this into the equation above, we get: (dh/dt) / (h - 3) = (35/8)h / (8 - 3)

Simplifying the equation will give us the value of dh/dt.