# Pythagoras and Trigonometry question

Watch
Announcements
#1
Could anyone help me with this question attached below.
My working so far is pretty minimal; I have just labelled the diagram with measurements.
Thanks
0
2 years ago
#2
(Original post by Roozie)
Could anyone help me with this question attached below.
My working so far is pretty minimal; I have just labelled the diagram with measurements.
Thanks
You probably know this already, but you need to find the cross-sectional area of the flow.
For this you need the area of the circle and the area of the segment that has no water,
http://mathworld.wolfram.com/CircularSegment.html
1
2 years ago
#3
A specific method and answer for this question would be as follows:

Diameter of circle is 30 mm so its radius is 15 mm so its area is 225 π.

Note that the horizontal line is 10 mm above the circle centre, so if you call this line AB and its midpoint M and the circle centre O, then the angle MOB will be arccos (10/15). So using double this angle, we can work out the area of the upper sector with radii OA and OB. We can also see that the area of the segment will be the area of this sector minus the area of the triangle AOB, which again you should be able to work out using either trigonometry of Pythagoras to get the length of AM and hence AB.

So finally you take this segment area away from the area of the circle to get the cross-sectional area of the water flow. Note that so far we've been working in mm and mm²; the question involves different units so you need to convert one way or the other. It's up to you which unit you choose as long as you're consistent. Personally I prefer to work in cm, so the mm² figure needs to be divided by 100 to convert to cm², and of course the 1.5 m becomes 150 cm. Also note that 40 litres = 40,000 cm³, and now you multiply your CSA by 150 to get the no. of cm³ flowing through per second, and finally divide this into 40,000 to get the number of seconds - and if it's in the hundreds, it would be appropriate to gives this as minutes and seconds.

Good luck! Get back to me if you still have problems.
1
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### Should there be a new university admissions system that ditches predicted grades?

No, I think predicted grades should still be used to make offers (696)
33.87%
Yes, I like the idea of applying to uni after I received my grades (PQA) (875)
42.58%
Yes, I like the idea of receiving offers only after I receive my grades (PQO) (392)
19.08%
I think there is a better option than the ones suggested (let us know in the thread!) (92)
4.48%