A rectangular prismatic tank has the following dimensions :length is 3 m, width is 2m . And depth is 3m .it is being filled with water and the surface level is rising at 20cm/min.what is the inflow rate of water at the tank ?

To find the inflow rate of water into the tank, you would need to calculate the volume of water being added per unit of time.

The volume of a rectangular prism can be calculated using the formula:

Volume = length x width x depth

Given:
Length = 3m
Width = 2m
Depth = 3m

Volume = 3m x 2m x 3m
Volume = 18 cubic meters

Now, the surface area of the water in the tank is equal to the length multiplied by the width, which is:

Surface Area = length x width
Surface Area = 3m x 2m
Surface Area = 6 square meters

And the rate at which the surface level is rising is given as 20cm/min. We need to convert this to meters per minute, so:

Rise rate = 20cm/min
Rise rate = 0.2m/min

The inflow rate of water into the tank is equal to the volume added per unit time. Since the surface area is increasing at a rate of 0.2m/min, the volume of water added per minute would be:

Volume added per minute = Surface Area x Rise rate
Volume added per minute = 6 square meters x 0.2m/min
Volume added per minute = 1.2 cubic meters/min

Therefore, the inflow rate of water into the tank is 1.2 cubic meters per minute.

To find the inflow rate of water into the tank, we need to determine the rate at which the volume of water is increasing.

The volume of a rectangular prismatic tank is given by the formula:
Volume = length * width * depth

For this tank, the length is 3m, the width is 2m, and the depth is 3m. Therefore, the initial volume of the tank is:
Volume_initial = 3m * 2m * 3m = 18m^3

The surface level of the water is rising at a rate of 20cm/min. This means that the depth of the water is increasing at a rate of 20cm/min. We need to convert this rate from centimeters to meters in order to match the units of the tank's dimensions.

1 meter is equal to 100 centimeters, so to convert 20cm/min to meters, we divide by 100:
Rise_rate_in_meters = 20cm/min / 100 = 0.2m/min

Now that we have the rise rate in meters, we can find the inflow rate of water by taking the derivative of the volume with respect to time. Since the volume of the tank is increasing with time, we are interested in finding the derivative of the volume with respect to time (dV/dt).

The volume of the tank is given by the formula:
Volume = length * width * depth

Differentiating this formula with respect to time (t), we get:
dV/dt = (d(length)/dt) * width * depth + length * (d(width)/dt) * depth + length * width * (d(depth)/dt)

Since the length and width of the tank are constant, their derivatives are zero. Therefore, our formula simplifies to:
dV/dt = (d(depth)/dt) * length * width

Substituting the values we have, we get:
dV/dt = (0.2m/min) * 3m * 2m = 1.2m³/min

Therefore, the inflow rate of water into the tank is 1.2 cubic meters per minute.