riddle that i need the answer to for extra credit?

Question

Mr. Sharp is finished dinner with his wife, his son, and his daughter.


It was his daughter's birthday, and his wife had made her a birthday cake that was 28 by 28 centimeters long, and 5 centimeters high. Icing covered the top and four sides.


Mr. Sharp: I'll cut the first piece for my daughter, and since she has turned 7 today, i'll start each cut 7 cintimeters from a corner and cut to the center.


Daughter: you didn't give me enough! that's not one quarter of the cake! and even if it were, i didn't get enough icing!


Son: you're too greedy! i think dad gave you too MUCH, you should give some back!


Mr. Sharp: well you're BOTH wrong. the piece is exactly one-fourth the volume of the cake and it also has exactly one fourth of icing on it.


who's right, and why??


please don't answer saying that i should do it myself. i've tried very hard and i don't know the answer. please help!

i think Mr. Sharp is right about the piece being the right size (28/7=4) but what about the icing? she has the right amount right?

Answer 1

ok... I'll tell you the answer... it's easy when you see it and it's hard to describe in writing, but I'll try!

It's a square cake... 28 by 28cm square...

All the cuts start 7cm from a corner and go to the centre...

The key here is that all the cuts start 7cm from -A- corner, and not always the same corner! in fact there are only 4 cuts made...

There are four 7s in 28, so draw yourself a 4x4 grid... it doesn't have to be 28x28, just as long as it's 4 squares by 4 squares...

Label the intersections (lines) up the side as 1 to 5 with 1 at the bottom.

Label the intersections along the bottom as a to e with a at the left like so:

5__________
4I__I__I__I__I
3I__I__I__I__I
2I__I__I__I__I
1I__I__I__I__I
..a...b...c..d...e

Now draw lines from: b1-c3, e2-c3, d5-c3 & a4-c3

You'll see that there are now 4 pieces of cake, each exactly the same, and each have the same icing on them too!

So the dad is correct!

Hope that helps explain things... It's one of those "think outside the box" riddles so don't worry that you didn't get it first time... So long as you tried! Besides... Isn't that what Yahoo Questions is for?!

Answer 2

All right, this is definitely an interesting problem.

Here's what I think.

If the dad starts 7 cm from a corner, cuts through the center to the opposite corner, then rotates the cake 90 degrees and does exactly the same cut through the middle using the same corner, then the cake is evenly divided into 4 parts, and each part has the same amount of icing.

If, however, the dad starts the second cut 7 cm from the same corner he started with on the first cut, I think you'd end up with kite-shaped pieces where 2 of the pieces are smaller than the other two.

I wish I could draw a picture here.

Answer 3

If you cut any distance for a corner, but aiming straight for the center, and then keep going all the way out, you are dividing the cake in two exactly similar pieces. They are oddly shaped, but still the same. Now, if you do it again 7 cm from the other corners (but always in the same direction) you have 4 identical pieces. It is as if you cut a circle in 4, and then, without moving the pieces, cut the circle again to convert it to a square. It does not matter what angle the square is relative to the cuts of the circle, you are removing the same amount from each of the 4 pieces.

Answer 4

Well, I am assuming some things, but will try to explain them.

I think they are all wrong.

If the dad only made three cuts (7cm, 14cm, and 21cm) then there are four equally sized pieces. However, the two end pieces have more frosting (7cmx28cm on top & 2(5cmx7cm) on sides for all four pieces). But the end pieces have an additional 5cmx28cm area on the ends.

I hope this helps, and I wish I could draw a picture for you on here.

Answer 5

Mr. Sharp is correct

Two things to consider: volume(cake) & surface area(icing)

Each piece has same amount of icing because each has a 21cm x 5 cm on one side, and 7cm x 5cm around the corner.

Each piece will also has the same volume because each piece has the same dimensions on all sides.

Answer 6

she got 1/4 of the cake and is right. to get one quarter the dad would have to cut 14 cm. form the corner and continue to the center. draw it out, and you will fully understand it.

Answer 7

1st 1/4 of a piece would be 14x14cm not 7x7, so each got 1/16 of the cake and not a quarter.

Answer 8

When i walk on the living i dont even mumble When i walk on the dead i mumble and grumble what are they.... fallen leaves

Answer 9

im not sure