Math Is Fun Forum

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Areas, circumferences, sectors of circles

Please help me out with this question.

My mom made a round cake with a 10 inch radius. She cut the cake into 16 equal slices. When 1 slice was left, my sister and I both wanted it, so we agreed to cut it in half, but I like the icing more than she does, so we decided to cut it the "other way." In other words, the two pieces would not be symmetrical. The inside piece would contain less icing, and the outer piece would contain the icing.

https://i.imgur.com/yQ2zLKX.png

1. Find the area of the whole cake.
A: π x 102^2. The area is 314.16

2. What is the area of one piece of cake?
A: I'm not sure what's being asked. Since the cake is split into 16 pieces, you just divide 314.16 by 16, right? That gives 19.635.

3. What is the area of a half-piece?
A: Half of a piece is 19.635 divided by 2? I'm not sure. That gives 9.8175.

4. What would the area of the whole cake be if it were cut into half pieces?
A: Not sure what's being asked.

5. What is the radius of a half-piece when it is cut as shown in the picture? (ie, where do I need to cut to make two equal halves out of a piece?)
A: ∑（´△｀○）I have no idea.

Thank you!

Last edited by simonmagusflies (2021-07-26 14:34:42)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Areas, circumferences, sectors of circles

hi simonmagusflies

Firstly what a brilliant diagram!  Did your Mum make that?   It looks delicious.  As you've had to slice it early do you need help eating the pieces before it goes dry?  Can you send a slice using 3D uploading?

I'm happy with your answers to Q 1,2 and 3.

Q4.  It's still the same cake.  Unless you can allow for the loss due to slicing the answer is still 314.16

Q5. If you just divided the cake into an inner and outer with equal area then you can easily calculate the area of the inner circle.  The outer would be a ring.  So you can work backwards starting with that area.  Divide by pi and the square root to get the radius.

But dividing like the diagram shows would give equal amounts of icing.  To get it all you would need to cut horizontally and give your sister the bottom half.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Re: Areas, circumferences, sectors of circles

Hi, thanks for the answer. The trick question does me in again!! 314.16 it is.

Still not sure about Q5, though. I'm no good with this stuff at all. I dunno whether what they mean when they say the radius of a half piece. Across the side or up and down?? I've got no clue at all.

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Re: Areas, circumferences, sectors of circles

Oh wait, so is the angle of the sector 22.5? Since the entire angle is 360, and there are 16 pieces, so 360/16 = 22.5, and now I've got to figure out the radius. But I'm a bit stumped. Gotta have the arc length to find the diameter, but can't find the arc length without the diameter.

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Re: Areas, circumferences, sectors of circles

darn, I'm definitely missing something, but I'm too dumb to know what

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Areas, circumferences, sectors of circles

You can forget about the sectors completely.  If the cake is divided into 16 pieces then there's an inner circle of 8 sectors and an outer ring of 8 equal pieces.  All you need is the radius of the inner circle.  If the 16 pieces are welded back together to make an inner circle and an outer ring you just need to find the radius of the inner circle.

Divide 314.16 by 2 to get the area of the inner circle.  Then:

You just need to solve that equation for r.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Re: Areas, circumferences, sectors of circles

Thanks! Sorry, I was being a major tard and missing out on stuff. It's like... 7.07?

Last edited by simonmagusflies (2021-07-27 20:19:30)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Areas, circumferences, sectors of circles

Yes! That's it.

B

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob