Wednesday, 7 August 2013

Malteser Maths

Ms Pears had a request from her daughter for a Malteser cake (photo from taste.com.au) for her birthday. She didn't know how many Malteasers to buy and this was causing her a lot of stress so we thought we would help her out.

She has already made the cake and it has a diameter of 20 cm and a height of 7cm. We need to tell her how many grams of Maltesers she needs to buy.

Some of our thinking:
  • We will need to know the weight of one Malteser. The packet is 40 grams - we will need to count the number of Maltesers and divide to calculate the weight of each Malteser. Or ... we could use miniature scales. 
  • We need to know the surface area of the cake. 
  • The two shapes that make up the cake are the circle, which is the top, and a rectangle.
  • How are we going to work out the size of the circle? We know the formula for the area of a circle is pi multiplied the radius squared. The radius of the cake is 10cm and pi is round about 3.14 so the area of the circle is 10 x 10 x 3.14 which is 314 cm squared. 
  • The sides of the cake, if you unfolded it would be a rectangle. The short side of the rectangle is 7cm. The long side of the rectangle is going to be the same as circumference of the circle. 
  • The formula is diameter multiplied by pi. 20 cm x 3.14 = 62.8 cm. This is the long side of the rectangle. The short side is 7 cm so the area of the rectangle is 439.6 cm squared.
  • So the total surface area that needs to be covered by Maltesers is  753.6 cm squared. 
  • We now need to know the surface area that one Malteser will cover. We thought they would cover a square shape rather than a circle shape.
  • We decided to estimate the diameter of a Malteser first.  Nadia said 4 cm, Lilli said 1.3 cm, Abby said 2.2 cm, Juliette says 1.5 cm Charlotte says 1.5 cm Alice says 1 cm, Emily says 2.7 cm, Lottie says 3.1 cm, Kate says 1.5 cm, Sarah-Rose says 1.5 cm. Some of us are very optimistic.
  • We measured Maltesers before we ate them. The measurements were:



  • We added them all together and divided to calculate the average (mean) diameter of a Malteser. It is 1.42 cm so we figured out each Malteser would cover a square approximately 2.016 cm square. We rounded this to 2 cm square. 
  • There were 20 Maltesers in a 40 grams pack so the average weight of a Malteser is 2 grams.
  • To work out the number of Maltesers needed we went 753.6 / 2. This equaled 376.8 Maltesers. 
  • We need 377 Maltesers and each is 2 grams so we had to multiply 377 by 2 so Ms Pears needs to by 754 grams.

10 comments:

  1. Interesting problem. I like your thinking. I hope you are now going to prepare a cake to test your theory. One factor to consider is whether the Maltesers will be fixed with icing - in which case the layer of icing (depending on the thickness- which will need to be enough to fasten a Malteser) may add one more Malteser in circumference and possibly height of the cake.

    I also wonder if the pattern you create on the cake will change the number of Maltesers. If you make a line straight across the cake or if you start with one in the centre and then create circles around that - this may change the number required.

    If I were making this cake I would use the formula : n=20 packets ÷ cake. r = snack. :)

    In case you are interested, here is Pi created with pies.
    http://www.youtube.com/watch?v=x4kyFKyCMv0

    G

    ReplyDelete
    Replies
    1. Photos of the cake coming. You are right about the icing but we also didn't allow for space of the icing squeezing up between the Maltesers. We are experimenting with patterns today. 8C

      Delete
  2. Jullian and Jono8 August 2013 at 08:50

    Hi 8c

    The cake looks great, what does yours look lik? How much did this all cost?

    It looks really nice what does it taste like?

    We see that You thought of this alot, your maths in this is interesting.



    ReplyDelete
  3. Hello 8C

    That cake looks great but did your cake have
    much similarity to the picture.

    I liked how you involved chocolate into maths
    because that way everybody would like maths.

    Keep up the good work
    From Nate

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  4. Hi 8C,

    This cake looks amazing. This mathematics looks so hard! How long did it take to work all of this out?

    Lottie

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  5. Wow I hope you get to bake this cake and do some more mathematical equations. Looks rather yummy

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  6. Wow Ms pears, Its going to be hard to match that cake! How long did it take to work out the Malteser problem and to put all the Maltesers on the cake?

    ReplyDelete
  7. Hi my name is Levi and my class is doing geometry for maths .i have a few questions to ask you .
    1.what is the area in meters of your class ?
    2.what is the perimeter in meters of your class ?
    3.what is the height of your class in meters ?
    4.how many desks/tables are in your class ?
    5.using the white board as north what position are your desks/tables in ?
    6.do you have any decorations in your class ?
    7.how many windows are in your class ?
    8.how many doors are in your class ?
    9.using the white board as north what position are your doors at ?

    From Levi
    Room 5
    Melville Intermediate
    Hamilton
    New Zealand

    ReplyDelete
    Replies
    1. Hi Levi,
      here are the answers to your questions
      1. Our classroom is 72m2
      2. Perimeter is 34m
      3. height is 4.10m at its highest point 2.3 metre at its lowest point.
      4. 16 desks, 1 large middle table and teacher desk and coffee table
      5. Some are facing north and some are facing south.
      6.Yes we have decorations
      7. 19 windows
      8. 3 doors,
      9. north, east and south

      Share our classroom with us after you build it.

      Thanks Lottie and Sarah Br.

      Delete
  8. Dia = 4cm!! - That's not a Malteser - it's the brown snooker ball!

    ReplyDelete

Thanks so much for your comment. We love hearing from you!

8C