Here, Can anyone help me solve this issue. I understand diameter of smaller circle = side of small square, and diagonal of small square = diameter of larger circle, and diameter of larger circle = side of larger square
in that way, i got A is larger
diameter of small circle = 4 (assumption)
length of small square = 4 (as above, equals to diameter)
diagonal of small square = 4 * root 2
diameter of large circle = 4 * root 2 ( as above, equals to diagonal)
length of large square = 4 * root 2 ( as above, equals to diameter)
i had very hard time deducing it, and i still find it confusing. What is the best way to do it? can someone do it in paper and submit it.
note: i also found somewhere the trick is both square and circle area are twice their smaller shapes. But i just know the trick, dont know its working.
The way you did seems the simplest to me maybe one of the tutors can give a simpler solution, I also don’t know about this trick to determine that the bigger ones are twice the size of the smaller ones. I am interested to know how much simpler it can get.
Let t denote the ratio between the bigger diameter and the smaller diameter.
We’re then comparing:
A: t^2 and B: 2 \cdot \frac{1}{t^2}
where t = \sqrt{2}
t = sqrt of 2, can you explain this ?
If blue is x then green is \sqrt{2} x. Thus, the ratio between diameters is t = \frac{\sqrt{2}x}{x} = \sqrt{2}
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also, can you once answer me how is Qty A: t^2 ?
area of small square = 1/2 * (smalll-diameter)^2
area of large square = ?
This diagram is confusing me
I get it, first Quantity A is the ratio of bigger square area to smaller square area which is Bigger dia squared to smaller dia squared similarly Quantity B is is the reciprocal of that smaller dia squared to bigger dia squared because we can cancel the pi/4 from the both. Now we are assuming Bigger dia to smaller dia is t so square of it t^2 and reciprocal is 1/t^2.
Finally
diagonal of smaller square = bigger dia
formula for diagonal is sqrt of 2 * a (side of smaller square) and smaller dia is just a (side of smaller square). So substitute this in t
t = ((sqrt of 2) * a) / a
The a in the numerator and denominator gets canceled leaving t = sqrt of 2
Hope you understood
Can you write out expressions for quantity A and quantity B in terms of the “big” and “small” diameters? I could give you a full solution, but it’s more instructive for you to stumble on it yourself (which is why my solution above was somewhat vague, assuming you’d fill in the intermediate steps), so that you don’t gloss over possibly salient points.
