# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 2022-12-08 08:22:44

undertaker
Member
Registered: 2022-11-04
Posts: 6

### geometry! one question :)

I've seen these questions on this site before, but they're not helping for me, so id appreciate some helo : )

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?)

I was told to use this formula, A = (n/360) * pi * r^2 but I don't know what n is... I know it's the central angle but I'm unsure how to find it!

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## #2 2022-12-08 23:24:27

Bob
Registered: 2010-06-20
Posts: 9,631

### Re: geometry! one question :)

hi undertaker

I'm assuming you mean this problem:

The size of the sectors is not relevent.  Let's say you had a slice one sixth of the cake and sub-divided as in the picture into two equal parts then <outer part> = <inner part> so 6 times <outer part> = 6 times <inner part>

= whole cake divided in two.

The area of the whole cake is pi r squared so we want the two parts to have area half pi r squared.

The inner is a smaller circle, so let's call it's radius 's'.  Then pi s squared = half pi r squared.

Cancel the pi on each side and you have s = Square root (half r squared) = root(2) . r

Hope that helps

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

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## #3 2022-12-09 05:59:40

undertaker
Member
Registered: 2022-11-04
Posts: 6

Thank you!

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