- #1
sophbell
- 2
- 0
Calculating Total Area Under a Trapezoidal Curve for Water Tank Fill Time
- Context: MHB
- Thread starter sophbell
- Start date
-
- Tags
- Tank Time Water Water tank
Click For Summary
Discussion Overview
The discussion revolves around calculating the total area under a trapezoidal curve representing the fill time of a water tank. Participants explore the geometric shapes involved, including triangles and rectangles, and how to compute their areas to find the total area under the curve.
Discussion Character
- Mathematical reasoning
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant, Dan, suggests that the area under the curve consists of a triangle and a rectangle and seeks clarification on how to sum these areas.
- Another participant proposes a method involving drawing horizontal and vertical lines to divide the area into a right triangle and two rectangles, questioning the area calculations for these shapes.
- There is a suggestion that the area might actually be a trapezium rather than just a triangle and a rectangle, indicating a potential disagreement on the geometric interpretation.
Areas of Agreement / Disagreement
Participants do not appear to reach a consensus on the shapes involved in the area calculation, with differing views on whether it is a triangle and rectangle or a trapezium and rectangle.
Contextual Notes
Some assumptions about the dimensions and relationships between the shapes are not fully articulated, and there may be unresolved mathematical steps in the area calculations.
- #2
- 2,020
- 843
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?sophbell said:
-Dan
- #3
HOI
- 921
- 2
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?
If that is less than 1000, subtract if from 1000. How wide must the second rectangle be so that its area is that difference?
- #4
Prove It
Gold Member
MHB
- 1,434
- 20
topsquark said:
Surely it's a trapezium and a rectangle...
Similar threads
- · Replies 2 ·
High School
Pumping water upwards into a large water tank
- · Replies 6 ·
- · Replies 2 ·
- · Replies 26 ·
- · Replies 15 ·
- · Replies 1 ·
- · Replies 22 ·
- · Replies 31 ·