A rectangular tank has square base of side l cm and height h cm. Given that the volume of tank is 8000 cm3, show that h = 8000/l^2
Relation between l and h is shown in the table below
l 10 15 20 25 30 35 40
h 80 35.6 20 12.8 8.9 6.5 5
A graph of h against l is then plotted.
The tank is constructed by first making rectangular framework of thin metal rods. Total length of ord used , L = 8l + 4h. By adding a suitable straight line to your graph, find smallest possible value of L
How do I obtain the equation of straight line? Thanks
Steps
(1) L = 8l + 4h
Re-arrange it into
4h = - 8l + L
h = - 8l/4 + L/4
h = - 2l + L/4
(2) Next, draw the line h = - 2l
Use two rulers, just the way 2 parallel lines are drawn.
Shift the line h = - 2l in parallel until it just touches the curve h = 8000/l^2
The interesecting point will be (l, h) = (20,20)
(3) Substitute l = 20 and h = 20 into
h = - 2l + L/4
20 = - 20(20) + L/4
80 = - 160 + L
L = 240
Hence, the smallest value of L is 240
ie the required equation of the line is 240 = 8l +4h
(4) Alternatively, make use of the line that just touches the curve.
The y-intercept of this line will be 60.
Since L/4 = 60,
so L = 60 x 4 = 240
Hence, the smallest value of L is 240
ie the required equation of the line is 240 = 8l +4h
The fun part of this question is that it is not the usual way of questioning in "O" E.Maths curve graph question ie asking students to find the gradient of the tangent or to find the co-ordinates of the point where the tangent and the curve meet.
This question requires the students to draw the line h = - 2l first and then to move this line in parallel until it just touches the curve. Next, to make use of the y-intercept of the line that just touches the curve to find the smallest value of L.
There is nothing wrong wwith the questioning of this question, my school exams like to play with these "revoluntionizing" qns.......just need some thinking
Hi,
There is more to objective and fair assessment than the setting of unusual questions that a great majority are going to be stumped and stressed ;)
Thanks!
Cheers,
Wen Shih
okays..........but as maths is a discilipline which allows one to excercise his/her thinking skills, settign higher order questions fits into the agenda
This question requires the knowledge of the use of a line to get a minimisation or maximisation solution of a given region formed by the use of inequalities or a given concave or convex arc.
This topic was tested in the 70s and 80s in E.Maths but this topic is no longer tested in the current E.Maths syllabus.