NeoPets Riddles (Lenny Conundrums) and Answers Here

This is very simply solved using integration. We can easily find the NE and SE edge functions, and integrate from 350 (half-way) to their intersect to the right and then simply double for the symmetry to find the answer.

- PeckyP -

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@starleogirl09,

Quote:

that's what i have been trying to figure out...

Ok, I see that the height of each triangle is half the radius of the circle. Not sure why, but it looks like it, and that's definitely the value they used. But the base? I don't see how they come up with sqrt(3)?

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@darkiaia,

http://wiki.answers.com/Q/Inside_a_square_a_circle_is_inscribed_what_is_the_ratio_of_areas_of_circle_to_that_of_square

I got my info off of this page... *shrug*

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The answer should be between 30% - 33% of the total area of the square. Which, if you think about it, makes sense.

- PeckyP -

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I found the following at Wikipedia useful:

http://en.wikipedia.org/wiki/List_of_integrals_of_irrational_functions

I used the first formula under the section "Integrals involving u = sqrt(a^2 - x^2)"

Namely, the integral of u is (1/2) * (x * u + a^2 * arcsin(x/a))

I used this to get the area of one of the indentation pieces that come in from the side. The "sort of" triangle that has two curved sides and one of the square sides as its third side.

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@PeckyP,

Yeah I see where I am wrong. My way would only make sense if it were a full circle contained within the square.

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the area of a triangle: 44838.11
multiply it by 2 then subtract from the 1/12 area of the whole circle .

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@PeckyP,

156800 cm aprox?

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@edstock,

That would have made my job so much easier if I knew that formula... Fortunately, I calculated it by myself, so we're all good on that front! =P lolz.

- PeckyP -

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has anyone figured out the base of the triangle? (http://mathcentral.uregina.ca/QQ/database/QQ.09.08/h/anthony1.html method)

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@darkiaia,

darkiaia wrote:

156800 cm aprox?

That is 32% of the area of the square, so it is in the range PeckyP was giving us. However, the range she gave is from 147000 to 161700 (30-33%), which provides an awful lot of answers to guess from.

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@edstock,

i wish i remembered how to use integrals...it's been so long!

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@darkiaia,

Somewhere close to there. 156800 is kind of a neat number for this type of question though. =P And just to note, it should be squared centimetres, not just cm. =P

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I used a method similar to the link posted with the 1/12 of a circle, and used trig to get the area of the triangles.

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@PeckyP,

Quote:

The answer should be between 30% - 33% of the total area of the square. Which, if you think about it, makes sense.

I hope you're right, because my answer is right in there. I decided to use sqrt(3) as a constant. Thanks for the integral advice, but since I took calculus over 35 years ago, it didn't do me much good. Smile

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@darkiaia,

ok...i made my way to the answer in a diff way and i got 268671.37 cm2
someone else have something like this?

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does anyone gets 154421.9044 (or approx) like i do?

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@edstock,

I just want to narrow it down for people who get that far. I'm not a silver platter (or if I am, I still need to cook in the oven more). =P lolz.

Anywho, I have to let people account for their own human error. I think this weeks correct guesses will be pretty low, so I want to keep my odds up there on big NP.

- PeckyP -

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@PeckyP,

yeah, that's a smart strategy; hopefully you get the answer right!

1 Reply

@rodrunner,

Quote:

the area of a triangle: 44838.11
multiply it by 2 then subtract from the 1/12 area of the whole circle .

Quote:

does anyone gets 154421.9044 (or approx) like i do?

Yes, that's what I came up with too.

1 Reply

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