A level maths help!!
I don't know how to do this question, I worked out that OB= 2root3 through pythagoras
I was thinking of working out the area of the segment because the 4 congruent triangles are right angled so r=2root3 and theta=pi/2... But this method cannot be correct since this is 8 marks
Any tips?
I was thinking of working out the area of the segment because the 4 congruent triangles are right angled so r=2root3 and theta=pi/2... But this method cannot be correct since this is 8 marks
Any tips?
(edited 1 year ago)
The figure didn't quite help, as it looks like an oblong* despite what the description says.
I think you might be missing a key piece of information, being arc BAD is part of a circle with center C.
With circles, centers and radii are your friend. In particular... Major spoiler:
Let's see if you make any breakthrough.
*We don't have a nice "formula" for areas of ellipses like the circle. I think we at least need integration.
I think you might be missing a key piece of information, being arc BAD is part of a circle with center C.
With circles, centers and radii are your friend. In particular... Major spoiler:
Spoiler
Let's see if you make any breakthrough.
*We don't have a nice "formula" for areas of ellipses like the circle. I think we at least need integration.
(edited 1 year ago)
Original post by tonyiptony
The figure didn't quite help, as it looks like an oblong* despite what the description says.
I think you might be missing a key piece of information, being arc BAD is part of a circle with center C.
With circles, centers and radii are your friend. In particular... Major spoiler:
Let's see if you make any breakthrough.
*We don't have a nice "formula" for areas of ellipses like the circle. I think we at least need integration.
I think you might be missing a key piece of information, being arc BAD is part of a circle with center C.
With circles, centers and radii are your friend. In particular... Major spoiler:
Spoiler
Let's see if you make any breakthrough.
*We don't have a nice "formula" for areas of ellipses like the circle. I think we at least need integration.
There is exact nice formula for area where a,b are semi and major radii of the ellipse.
It's the perimeter that doesn't have a nice formula.
Original post by RDKGames
There is exact nice formula for area where a,b are semi and major radii of the ellipse.
It's the perimeter that doesn't have a nice formula.
It's the perimeter that doesn't have a nice formula.
Huh, that's neat. Thanks!
i tried it but i got stuck i think i have some misunderstanding with the areas overlapping but i got to 32pi-8root3 idk where to go from there if anyone could enlighten me that'd be great hahaha
for context i worked out the area for the rhombus in 4 right angles then worked out the angle at C which i assumed i equal to A due to symmetry to be 60 degrees then i worked out the areas of each "sector" to be 16pi then multiplied by two because there are 2 sectors (imagined from the arcs) then i did 32pi-8root3 but i know i went terribly wrong somewhere
for context i worked out the area for the rhombus in 4 right angles then worked out the angle at C which i assumed i equal to A due to symmetry to be 60 degrees then i worked out the areas of each "sector" to be 16pi then multiplied by two because there are 2 sectors (imagined from the arcs) then i did 32pi-8root3 but i know i went terribly wrong somewhere
(edited 1 year ago)
Going off on a tangent, the question is a modification of one of Eucllid's basic propositions
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI1.html
and "famously" reared its ugly head as last years hard gcse (edexcel paper 1) question.
For this one, a sketch of one of the circle sectors with two of the shaded areas marked on should make it possible to pretty much write down the answer as Tony alludes to. Generally for questions like this, a good/insightful sketch is worth most of the marks.
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI1.html
and "famously" reared its ugly head as last years hard gcse (edexcel paper 1) question.
For this one, a sketch of one of the circle sectors with two of the shaded areas marked on should make it possible to pretty much write down the answer as Tony alludes to. Generally for questions like this, a good/insightful sketch is worth most of the marks.
(edited 1 year ago)
Original post by tonyiptony
The figure didn't quite help, as it looks like an oblong* despite what the description says.
I think you might be missing a key piece of information, being arc BAD is part of a circle with center C.
With circles, centers and radii are your friend. In particular... Major spoiler:
Let's see if you make any breakthrough.
*We don't have a nice "formula" for areas of ellipses like the circle. I think we at least need integration.
I think you might be missing a key piece of information, being arc BAD is part of a circle with center C.
With circles, centers and radii are your friend. In particular... Major spoiler:
Spoiler
Let's see if you make any breakthrough.
*We don't have a nice "formula" for areas of ellipses like the circle. I think we at least need integration.
...but it's not an ellipse. DAB and DCB are both circular arcs, with centres C and A respectively. The area of one of the four shaded sections can be found by subtracting the area of triangle CBA from the area of the sector CBA.
(edited 1 year ago)
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