#Math IA in IB

46 messages · Page 1 of 1 (latest)

pastel flax
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Guys I am doing modelling for my Maths IA. I am modelling the taj mahal. But I don't have a single clue as to how to start modelling. I will also calculate its volume using volumes of revolution with integration. Anyone got any ideas?

lofty igloo
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oh my days u need to use integration for this?

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okay ref pic

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gimme a moment

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I'm assuming I can model the centre piece like this

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oh wait tbh a circle would be better to model the curve

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brb

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maybe this is better? the top semicircular eqn is

(x-10)² + (y-10)² = 100 where it's range is restricted 10 ≤ y

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welp this is the best I could get

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from there u can u can integrate with respect to x by making y the subject of the equations of the curves

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then im assuming u should be able to integrate and find volume?

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for the larger part
eqn of circle:
(x-10)² + (y-10)² = 100
(y-10)² = 100 - (x-10)²
y-10 = ±√[100 - (y-10)²]
y = 10 + √[100 - (y-10)²] (u can reject the negative one bc the portion of the circle above y = 10 has positive in front of the √)

it's volume hence
= π∫ y² dx
= π∫ { 10 + √[100 - (y-10)²] }² dx

lower limit = 0
upper limit = 20

expand and simplify

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well not too sure on the scale so the limited can be changed based on how u wanna scale down the actual model on a graph

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this is assuming that a volume is formed by rotating the area under graph by 2π radians about the x-axis

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for the rectangle under he big semicircle, when rotated 2π radians about x-axis u will get a cylinder with radius 10 and height 20

so volume = π(10²)(20)

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do the same for the smaller circle and smaller rectangle but be sure to take the sum of these 2 and ×2 to account for the other side of the Taj Mahal

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this is so tedious and im sure my model is very inaccurate too 💀

pastel flax
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but thank you so much for your help! I really appreciate it 🙂

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This gave me a lot of ideas

pastel flax
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i am struggling to make the contract curve at the top of the dome. thankfully i dont need to model it in great detail, just to the best of my abilities 😃

lofty igloo
lofty igloo
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there's a +3 behind the red graph eqn and a -3 behind the blue graph eqn

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this looks like a nicer model for the curved portion

pastel flax
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Ooh okay!!

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Thank you so much! I was hella stressed for this

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Its actually not that difficult

lofty igloo
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oh no problem at all, I always have fun doing math problems

alpine shadow
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sheeeeesh gj @lofty igloo

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I love how u approached this it rly is an interesting problem

lofty igloo
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well math is all about finding the most refined and tbh most elegant method of solving problems thru a step-by-step approach :)

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haha but yea first time i've seen integration being used to model and find the volume of a real life building

pastel flax
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i was originally also thinking of finding its surface area but then i realised its way above my field of expertise,,, even my math teacher strongly adviced me to not do it

lofty igloo
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ahahah yea, i wouldn't even know how to start for that 💀

lofty igloo
pastel flax