Wednesday, November 12, 2008

Round 287

I think this may be the final version.

Tier 1: r1 = d1/2 = 6 in (bottom)
Tier 2: r2 = d2/2 = 5.25 in (middle)
Tier 3: r3 = d3/2 = 4.5 in (top)
Height: h = 1.5 in (height of a layer)

V(cake) = pi * ((r1-1/3)^2 + (r2-1/3)^2 + (r3-1/3)^2) * (3*h)

V(frost_side) = pi * (2/3 r1 + 2/3 r2 + 2/3 r3 - 1/3) * (3*h+1/2)
V(frost_top) = pi * (r1^2 + r2^2 + r3^2) * 1/3
V(frost) = V(frost_top) + V(frost_side)

V(jam) = pi * ((r1 - 1/3)^2 + (r2 - 1/3)^2 + (r3 - 1/3)^2) * 1/2

weight = V(cake) * 0.35 + V(frost) * 0.48 + V(jam) * 0.6

cal = weight * 53.4

Remember not to round before the the final answer. Good luck.

38 comments:

Rodrunner said...

5-digit number? that has numbers 1 3 6 2?

Mellow said...

I don't get it. This is impossible.

Ademar said...

Mine was 5-digit number. With the numbers 1 7 3 and 4

Ademar said...

Not 7 xD



8!

LC Solver said...

All I can say I have 5 digit numbers with 1 beginning. Depending on how you interpret the problem, you may get different results...

Ademar said...

I think I rounded too much :S

Rodrunner said...

what is your last digit. i might not get it becoz of the rounding off. LOL any clue of the last digit?

Mailbox said...

The Jam layers make the level 2&3(mid & top) higher of 0.25 inch, so the Height of Frosting layers of level 2&3 should be 1.75 inches, rather than 1.5 inches.

Does this makes sence? I'm not sure about it because the what the question states is a bit misleading.

Rodrunner said...

i used the 3 formula for the vfrost_side and they have different results (im referring to their, decimal points)

so any clue about your last digit lc solver?

LC Solver said...

rodrunner, my last digit and your last digit seem to be the same so I think you're right on rounding off.

However, the way I interpret the problem, not sure correct or not.

Eeyore said...

Am I the only one who thinks there are 9 layers to the cake... Problem states 3 tiers and each tier has 3 layers...

LC Solver said...

Eeyore, you're right. I am gonna rework this problem. Thanks

edstock said...

After reading it, I think we have 9 layers of cake (each 1.5 inches thick) and 6 layers of jam (each 1/4 inch thick). I also calculated with 3 layers of frosting and 3 cylinders of frosting.

The layers of cake and jam have diameter 2/3" less than 12, 10.5 and 9, so I used 11 1/3, 10 5/6 and 8 1/3 as my diameters.

For the frosting, I used layers of diameter 12, 10.5 and 9, thickness 1/3". I also did 3 cylinders for the sides. To find the areas of the cylinders, I took the areas of the layers and subtracted the area of a layer of cake within the tier. I took the height of each cylinder as 5 inches - 3 x 1.5 + 2 x .25 (3 cake layers and 2 jam layers).

LC Solver said...

edstock, that is another to interprete the problem. I'll try to incorporate into alternative solution

Rodrunner said...

i guess, there is a BIG difference between:

V(jam) = pi * (r1^2 + r2^2 + r3^2) * 1/2

and

V(jam) = pi * ((r1 - 1/3)^2 + (r2 - 1/3)^2 + (r3 - 1/3)^2) * 1/2

LC Solver said...

yeah that is very huge because the jam weights a lot (0.6 compared to 0.35 and 0.48)

Niko said...

I worked my own formula and I get a five digit number starting with 2 and ending with 6...

MelissaC said...

I got a 4-digit number (high one, starting with a 9....) =/

Mailbox said...

Now is a bit clear about the cake's stucture, but still confusing about your answer.

The question said "Each layer of cake was 1.5 inches thick. "

NOT Each “tier” of cake was 1.5 inches thick.

So, the height of each tier is not 1.5 inches, but should be 1.5*3 + 0.25*2 =5 inches? or even add 1/3 inch of frosting?

LC Solver said...

thanks mailbox. I just discovered and fixed that. I messed up between tier and layer badly. I think it is the final version!

Niko said...

yes that's how I understood it, also notice how is said for instance the TOTAL length of the first tier is 12"... That probably means that it INCLUDES the frost of 1/3"... The way I calculated that, the cake without the frost has a total length of 12 - (1/3 * 2)

(1/3 * 2) as the frost is on both "side" of the total length. Your cake without the frosting is 11.33333" (r = 5.66666)

LC Solver said...

the problem never mention the height of the tier so we don't need to worry about that...

edstock said...

I think I'm close to Nike, but I get an 8 at the end.

theCrew said...

i got a 5 digit number starting with 2? anyone got that too?

DrStevo said...

First: figure out the total volume of each tier. Second: the volume of cake only and jam only for each tier. Third: subtract to find the volume of icing only for each tier. THEN add to get the total cake, jam and icing volumes. Then convert to ounces of cake, jam and icing to get a total weight of the completed cake multiply by 53.4 cal/oz and got a 5 digit figure beginning with 2.

Megan said...

I fot a 5 digit number starting with 1 and ending with 3.

Anyone else?

TODO SEPTIMO said...

whats is the answer?

Will said...

Are the tiers frosted/covered on the bottom? It said top and sides... does sides include the bottom?

Ademar said...

59130,26021625?

ll*believe in myself-ll said...

my first digit is 2 and last digit is 8.

edstock said...

I have the same first digit 2 and last digit 8 although it worries me that my unrounded answer is less than .02 away from being rounded up instead.

Reena said...

I got a five digit number starting with 2 and ending with 8 using my own calculations. I consider myself a pretty good math student and am fairly confident of my answer. ^^

(I didn't round until the last answer (left all my calculations in the calculator to at least 5 decimal places) so your answer might be off by 1-3)

vmpirebtch said...

i had a 5 digit number starting with 2 ending with 4 T.T im good at math and i get how to do it but i think i made careless errors

Caitlin said...

Ok, I did all of the steps at the top of the page and my answer was . . hmm .. why haven't you guys put your whole ans. down? ok, so I wont either . . but, my calorie no. started with a 1 & ended with a 3 . . Hopefull I'm right . . Goodluck to you guys too and thanks for all your help in preious conundrums.

Caitlin said...

Lol, one more message . . Sorry about my bad typing XD

edstock said...

They liked my answer of 29508.

Eric said...

The solution as runnable Perl code.

ultrablue7 said...

Thanks!!!!!!!!!
My answer was right and I get a silver trofeum, the avy and the cake!
Yuhuuuuuuu!!!!!!!!
:D