Comments on: Circular Measure – Like Sailors To Sirens

By: TJK

TJK — Sun, 08 Nov 2009 04:09:04 +0000

Why did the chicken cross the road [12]

Answer: Because the chicken wanted to get to the other side of the road (12 marks)

anyway, nice short question...and a nice website

By: Tan Jye Yee

Tan Jye Yee — Sun, 12 Aug 2007 06:27:17 +0000

I'm a J2 student... Shame on me. Haha.

By: Miss Loi

Miss Loi — Sat, 11 Aug 2007 17:04:37 +0000

Jye Yee, tidied up your workings for readability and added some comments in red.

Great work but Miss Loi thinks you're overaged! :S

Now open your mouth and standby for marshmallows ...

By: Tan Jye Yee

Tan Jye Yee — Sat, 11 Aug 2007 11:56:40 +0000

Let the point of intersection of the two circular parts be X.

XC=XD=radius=5 cm

Therefore, triangle XCD is an equilateral triangle.

Yes this is the crucial part! Students need to know how to 'partition' the area first. In this case it's the triangle plus the two sectors. Next students need to know that this triangle is equilateral, either by appreciating that XC and XD are radii of the quadrants (like you mentioned) or by simply appreciating that the angle DXC subtended to the intersection point of the two quadrants is 60^o.

area of triangle XCD=0.5*5*5*sin 60=10.83

Since the sectors of a circle are identical, total area of two sectors=

Area of sector = , reproduced for the benefit of readers here

Shaded area=

Minor correction: unit of area should be cm² instead of units³ as you've written. Any reason why you wrote units³?

This question can also be solved via integration, using the equation of the circle as x²+y²=5²
Integrate y with respect to x, with lower limit 0 and upper limit 2.5, then multiply by two.

Substract this from 25 cm² to get the final answer.

Equation of circle is not in the O-Level syllabus this year. But then again you might be in Sec Three. But if you are indeed, you shouldn't have learnt integration yet. So Miss Loi concludes that you're overaged!!!

By: Miss Loi

Miss Loi — Sat, 11 Aug 2007 10:18:36 +0000

Impressive young jedi.

But show working you must, or get a marshmallow you won't.

By: Tan Jye Yee

Tan Jye Yee — Fri, 10 Aug 2007 13:05:19 +0000

1.08 units^3 [3 s.f.]

By: Miss Loi

Miss Loi — Fri, 27 Jul 2007 15:49:41 +0000

Abhinav, you're supposed to be doing the question on the shaded area - not join the chick on the roadside admiring Ferrari cars! lol

Having said that, your reasons (for the chick's decision) alone are enough to get you a PhD!

P.S. Chicks in Singapore chicks are all blessed with superpowers! hahaha

By: Abhinav Sood

Abhinav Sood — Fri, 27 Jul 2007 06:45:12 +0000

distance traveled by cat = 10m at a speed of 3.5kph (or you can say at 35/36 meter per second)
Therefore, time taken by the cat to reach the chick is 10/(35/36)=10.28s

Similarly, distance covered by the ferrari enzo car at 350kph(3500/36 meter per second)=1km=1000m
Implies, time taken by the car to reach the crossing point=10.28s again !

That implies that the chick crossed the road so that when the car is at the crossing point the cat would be forced to stay on the other side of the road be'cuz at that very instant the car would be crossing right in front of the cat.

This problem was fairly easy, except the one thing that I couldn't understand... HOW DID THE CHICK DO IT... Must have got some superpowers to judge the distances ! and do all the calculations while its life is jus on the tip off his head ready to jump-off anytime as the cat is chasing her ... Hha, Thats what got me interested in answering this one.

Good going Miss Loi (I wonder why you like to converse as a third person about yourself ! )
Keep educating the students, make a better world tomorrow.