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

AI Thread Summary
The area under the curve for the water tank fill time consists of a triangle and a rectangle. To calculate the area, a horizontal line at "100" and a vertical line at "2" are drawn, creating a right triangle with legs measuring 2 and 200, and a rectangle with width 2 and height 100. The area of the triangle is calculated, and if the combined area of the triangle and rectangle is less than 1000, this value is subtracted from 1000 to determine the required area for a second rectangle. The discussion emphasizes the need to find the width of this second rectangle to achieve the desired area. Overall, the focus is on accurately calculating the total area under the trapezoidal curve.
sophbell
Messages
2
Reaction score
0
image.jpg
 
Mathematics news on Phys.org
sophbell said:
View attachment 11490
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...
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Similar threads

B Pumping water upwards into a large water tank
Replies
3
Views
2K
MHB If both pipes are used together, how long will it take to fill 2/3 of the tank?
Replies
9
Views
2K
Measuring the water volume in a small tank with a manometer
Replies
26
Views
2K
Improving heat transfer in domestic hot water tank?
Replies
15
Views
4K
Time to Empty a Tank with Water Flowing at 2h kg/s
Replies
1
Views
1K
Fluid dynamics problem: Equalize the volume of water in tanks at differing heights
2
Replies
50
Views
7K
How Much Work to Fill a Cylindrical Tank with Water?
Replies
22
Views
3K
I Water Tank Overflow Air Piston concept/question
Replies
31
Views
2K
MHB Emptying and filling a tank word problem.
Replies
2
Views
6K
MHB Find Rate Water is Pumped into Tank | NatyBaby's Question at Yahoo Answers
Replies
1
Views
6K

Hot Threads

Recent Insights

Back
Top