Parallelogram 1 Level 1 24 Aug 2023The mathematics of cake

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. a portmanteau word combining parallel and telegram. A message sent each week by the Parallel Project to bright young mathematicians.
  • Tackle each Parallelogram in one go. Don’t get distracted.
  • Finish by midnight on Sunday if your whole class is doing parallelograms.
  • Your score & answer sheet will appear immediately after you hit SUBMIT.
  • Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.

1. The scientific way to cut a cake

Watch this Numberphile video about the best way to cut a cake and answer a few questions.

(If you have problems watching the video, right click to open it in a new window)

2 marks

1.1. What problem is Alex trying to solve?

  • Minimise cake being wasted.
  • Minimise cake becoming dry.
  • Minimise the number of crumbs.
  • Minimise the number of slices.
  • Minimise the risk of injury caused by cake.
  • (Not answered)
2 marks

1.2. To solve the problem, according to Alex, what is the best way to slice the cake?

  • Blindfolded.
  • Make two cuts that make a V-shape.
  • Make two parallel cuts that remove a centre strip of the cake.
  • Cut the cake horizontally.
  • Use a chainsaw.
  • (Not answered)
2 marks

1.3 This video does not discuss the volume of a cake, but perhaps you can calculate the volume of a circular cake with radius 20cm, and a height of 10cm ... to the nearest cubic centimetre (cc)... and assume that pi has a value of 3.14159.

Show Hint (–1 mark)
–1 mark

A round cake is effectively a cylinder. The volume of a cylinder is the height multiplied by the area of the top (or bottom surface). The area of a circle is pi multiplied by the square of the radius.

Correct Solution: 12566 cm3

The cake shape is a cylinder, which could also be called a circular prism. The volume of a cylinder (or any prism) is equal to the area of one of the ends multiplied by the height (or length).

If you have been taught about π, then you might know that that the area of a circle is πr2, so the total volume is:

πr2×h=π×202×10=12,566 cm3

2. A cake conundrum

Watch this video and find out how to solve the cake conundrum. pause the video before the end to see how you can solve the problem before the answer is revealed.

(If you have problems watching the video, right click to open it in a new window)

2 marks

2.1 The cake should be cut into shapes that look like which letter:

  • L
  • U
  • V
  • T
  • I
  • (Not answered)
2 marks

2.2 When the cake is cut into these shapes (L,U,V,T, or I), how much of the whole original square cake does each piece represent?

  • 116
  • 117
  • 316
  • 317
  • 516
  • (Not answered)

The original square piece is a quarter of the whole cake. The remaining 3/4 is divided into four pieces, so each of those pieces must equal a 316 of the original cake.

Before you hit the SUBMIT button, here are some quick reminders:

  • You will receive your score immediately, and collect your reward points.
  • You might earn a new badge... if not, then maybe next time.
  • Make sure you go through the solution sheet – it is massively important.
  • A score of less than 50% is ok – it means you can learn lots from your mistakes.
  • The next Parallelogram is released at 3pm on Thursday September 14th.
  • Finally, if you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelograms.

Cheerio, Simon and Ayliean.