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**kayalexis****Guest**

Hello,

I am having some troubles with this one question. I will post the answer I got below the question, but I am unsure if it is correct. I am supposed to fully explain my answer, so sorry if it a little wordy.

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?)

To get the radius of a half-piece, you must figure out the radius for the whole cake. I got the radius by taking the area of the whole cake (314.159) and dividing that by PI (3.14159). I then got 100. I then took the square root of that to get 10. 10 is the radius of the whole circle. (The formula to get radius is A/PI = r^2). Now that I have my radius, I can plug it into the equation. 314.144 = PI(10)^2. This then equals 986.958. This rounded equals 987 in^2.

Thank you!

Kayla

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,508

hi kayalexis

Welcome to the forum.

What is the radius of a half-piece when it is cut as shown in the picture?

I'm having trouble understanding what this picture is like. Please would you describe it in words so I can think about whether what you are doing is correct.

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 Bundy

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**kayla1dance****Member**- Registered: 2018-01-10
- Posts: 44

Hello,

How do you upload a picture so I can show you the problem and the cake they are referring to?

Thanks,

Kayla

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,508

hi kayla1dance

I made a set of instructions back in 2015. They still work. Here's a link to the post:

http://www.mathisfunforum.com/viewtopic … 40#p352440

I'm really pleased that you have decided to join us.

Welcome again!

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 Bundy

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 27,901

Hi kayla1dance,

**Welcome to the forum!**

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**kayla1dance****Member**- Registered: 2018-01-10
- Posts: 44

Hello,

Here is a link to the image with the question and some pictures. I am working on #5. I have gotten all the other answers correct. In the last post, I posted what I believe the answer is. If you could let me know if that is correct, that would be awesome!

Here's the link: https://imgur.com/tdFRvsY

Thanks,

Kayla

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,508

hi kayla1dance,

That's great; thanks for the picture.

What you have written seems, to me, to be back to front. You have used the area to get the radius, whereas you must, in fact, have used the radius to get the area.

It is not relevant that 15/16 has been eaten. You can just determine how to divide the area of the whole cake in half. Then every slice will have the potential to be split in half.

I think you need these steps:

(1) Calculate the area of the cake.

(2) Calculate half this. This will give you a inner circle which has half the area and a ring which has the other half.

(3) Work backwards from this inner circle to determine what radius it must have. (note: The answer must be under 10)

Bob

Note about posts containing links. The way you have done this means any member is linked to all the imgur image posts. I don't do it like this because some of our members are too young to be looking at imgur. It has an age limit restriction. The link I gave to an earlier post shows how to create a bc code link. This image appears in the post and any viewer can see it without having to go to the imgur site.

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 Bundy

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**kayla1dance****Member**- Registered: 2018-01-10
- Posts: 44

Hi bob bundy,

I have gotten the area of the circle which is 314.159. I calculated half of that and got 157.079. (I took 314.159 and divided by 2). I am confused on what the next step is and how you work "backward".

Thanks,

Kayla

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,508

hi kayla1dance

Ok, that's good so far. The area of the whole cake is now divided into an inner circle (area = 157.079) and an outer ring (also area = 157.079). don't worry about the sectors for now.

So if r is the inner radius:

Solve this for r.

Bob

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 Bundy

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**kayla1dance****Member**- Registered: 2018-01-10
- Posts: 44

Hi bob bundy,

Okay so I took PIr^2 = 157.079 and I solved. I took the formula A/PI = r^2. I then plugged in my numbers. I got 157.079/ PI = 49.999. I then took that and got the square too to find r. (49.999 = r^2). After getting the square root the answer is 7.071. So, the radius of a half-piece is 7.071.

Is this correct?

Thank you again,

Kayla

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,508

hi kayla1dance

Well done! That looks good to me.

Bob

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 Bundy

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**kayla1dance****Member**- Registered: 2018-01-10
- Posts: 44

Hello,

Thank you for your cooperation. If you could delete this post as well that would be awesome!

Thank you for all the help,

Kayla

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