# Calculating Total Area Under a Trapezoidal Curve for Water Tank Fill Time

• MHB
• sophbell
In summary, the conversation discusses finding the sum of the area represented under a curve, which consists of a right triangle and two rectangles. By dividing the area with a horizontal and vertical line, the triangle and first rectangle can be identified. The remaining rectangle's width must be determined in order to find the total area.
sophbell

sophbell said:
The area represented under the curve is a triangle (up to t = 2 hours) plus a rectangle. How do you find the sum of that area?

-Dan

Draw a horizontal line at "100" all the way across. Draw a vertical line at "2" all the way up and down. That divides the area into a right triangle with one leg of length 2 and the other of length 200, a rectangle with width 2 and height 100, and another rectangle with height 300 and unknown width. What is the area of the triangle and the first rectangle?

If that is less than 1000, subtract if from 1000. How wide must the second rectangle be so that its area is that difference?

topsquark said:
The area represented under the curve is a triangle (up to t = 2 hours) plus a rectangle. How do you find the sum of that area?

-Dan

Surely it's a trapezium and a rectangle...

## 1. How do you calculate the time it takes to fill a water tank?

The time it takes to fill a water tank can be calculated by dividing the volume of the tank by the flow rate of the water source. This will give you the time in hours it takes to fill the tank.

## 2. What factors affect the time it takes to fill a water tank?

The main factors that affect the time it takes to fill a water tank are the size of the tank, the flow rate of the water source, and any obstructions or restrictions in the water flow. Other factors that may play a role include the temperature and viscosity of the water, as well as the pressure of the water source.

## 3. How can I increase the speed of filling a water tank?

To increase the speed of filling a water tank, you can either increase the flow rate of the water source or decrease the volume of the tank. You can also remove any obstructions or restrictions in the water flow to improve the filling speed.

## 4. Is there a formula for calculating the time to fill a water tank?

Yes, the formula for calculating the time to fill a water tank is: Time = Volume / Flow Rate. Make sure to use consistent units for volume and flow rate (e.g. liters and liters per hour) to get an accurate result.

## 5. Can the time it takes to fill a water tank vary?

Yes, the time it takes to fill a water tank can vary depending on the factors mentioned above. It can also vary if there are any changes in the water flow rate or if there are any changes in the size or shape of the tank. Additionally, external factors such as power outages or equipment malfunctions can also affect the filling time.

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