500 million points for anyone who can solve this maths problem

[da_beast]

Ah, i think i had right the first time I tried it in the calculator then. I just wasnt sure if that 2.54 was correct because I didn't understand that second picture. I'll see if I can do it on paper when I get home for fun.

That would be excellent. If you can do it on paper without using the aquarium calculator your better at maths than me lol

I don't know the formula to work it out

[Toyman]

I asked my old lecturer and he said the sensor area to be calculated is the whole of the top picture in the diagram.

I can do it using the aquarium website but i still dont know how its technically done.

i just looked on aquarium, and i think miniq's got it right


The surface area of the rectangle is 9.02, and inputting the given figures on aquarium gives 11, which includes just 1 half of the round segment, so with 2 parts of it you end up with an extra 1.98, i.e 12.98.

i guess the key here was the formula to get the area of the rounded segment, which i reckon isnt something most people would know off the top of their head lol

(I did it manually using straight triangles to approximate, and ended up with about 11.94, so it would make sense that including the round portion adds a bit more to the total)

[da_beast]

Yeah... my bad - however you can do it using the sensor seperation 2.54 from the second diagram. This ****'s causing brain overheat - been 20 years since I hadda do this kinda thing.

Lmao. I've been trying to crack this for 2 days. In my spare time too lol. It's annoying the life out of me

[da_beast]

i just looked on aquarium, and i think miniq's got it right


The surface area of the rectangle is 9.02, and inputting the given figures on aquarium gives 11, which includes just 1 half of the round segment, so with 2 parts of it you end up with an extra 1.98, i.e 12.98.

i guess the key here was the formula to get the area of the rounded segment, which i reckon isnt something most people would know off the top of their head lol

(I did it manually using straight triangles to approximate, and ended up with about 11.94, so it would make sense that including the round portion adds a bit more to the total)

Do you have a copy of the working using triangles and how you did it?

[Toyman]

Do you have a copy of the working using triangles and how you did it?

The triangle method is wrong, because its only an approximation as i wasnt aware of the formula for the surface area of a elliptical object, which is the shape of the 2 round segments if they were combined. Using the correct formula like on aquarium will include the round portions which the triangle wont capture.


Not sure if im repeating something you already know: but my understanding is that the surface area of the total figure would be the area of the rectangle in the middle plus the area of both rounded segments. The area of the rectangle is 2.54 * 3.55 = 9.02.

Then using aquarium, you can input the figures from your diagram to give the area of the rectangle plus one rounded segment, which gives 11, which means the area of one round segment must be 1.98. So the total area must be 9.02 + 1.98 + 1.98 = 12.98

Not sure if thats what ur asking for, but imo thats the logic behind it

As for the formula, i dont know exactly why it is what it is, but aquarium gives it as
[Area(circle segment) =r.r.(theta - sin(theta))/2] - If you manually put this into a calculator, it would probably give you 1.98, but i just used the calculation form

[Citizen Koba]

I'm pretty sure we don't have sufficient info to calculate the area of the curved segments - we don't have (and can't calculate) a radius for them (ie we don't have a centre point for either of the curves) and without that we can't reliably calculate area.

Does the TS know what the hatched area (roughly square in the middle - with a couple of sections removed where the probes emerge) represents? If the hatched area happens to represent the sensor things obviously become somewhat easier.

[sugarsmosley]

thank god im not taking math next year

[Toyman]

OK Everyone

I think i might have found the answer to this once and for all lol:

The objective is to find the area of the top figure, which appears to be a rectangle with 2 rounded segments at the end. So the area of the whole figure must clearly be the area of the rectangle and the 2 round portions.

The width of the entire figure is given as 4.195, and the height as 3.55.

From the bottom diagram, we can clearly see that the width of the rectangle is 2.54. This means that the area of the rectangle must be 2.54 * 3.55 = 9.02

As we now have the area of the rectangle, we need to find the area of the 2 round segments.

As noted, the 2 round segments, if placed together, do not actually form a circle. But they do form an ellipse, and we can deduce the maximum width and height of this ellipse by using the dimensions of the whole figure and the rectangle.

Since the whole figure is 4.195 wide, of which 2.54 is taken by the rectangle, this means that the maximum width of the 2 round parts must be 4.195 - 2.54 = 1.655. The max height of the ellipse is the same as the rectangle, 3.55.

As per google, the formula for the area of the ellipse is ( pi * 0.5W * 0.5H )

As we have deduced the width and height above, the area of the round segments must equal to [( pi * (0.5*1.655) *(0.5*3.55)], aka 4.61

Now that we have the round section at 4.61, and the rectangle at 9.02, the area of the whole figure must be 9.02 + 4.61 = 13.63.

P.S - Miniq, if you ever read this - i think you had the right approach, just that acquarium only gives whole numbers in its answers, so it leads to a bit of inaccuracy.

[DoktorSleepless]

My math must be absolutely dreadful. I've probably forgotten a bunch of math rules. Im embarrassed. Doing it by hand and following the steps from that aquarium page:

I got 2.317 for radius
I got 20.5764 for theta
And I somehow got 46.864 for a circle segment. That's obviously wrong.

Anyone else going to give it a shot?

EDIT: Here's my work

[miniq]

toyman I see where you're coming from with the ellipses idea but it's wrong sorry :| The height of the minor axis (y) is unknown... you are taking the rectangle height as that axis...

doktorsleepelss - your value of 'X' goes from 2.54 to 0.8275...lol it should remain 0.8275... (in the radius formulae)