Maths Camp

Challenge 1 – Are you ready to be Bob the Builder? (taken from here)

Back in 2010 a massive sink hole swallowed a building a neighbourhood in Guatemala (story here).

If you want to find out more about how is a sink hole form watch this video

You challenge is to work out how much concrete you would need to fill the hole and then find out how much it would cost.

Where to start:

Discuss with a partner the following questions

  • What is a guess that is too low?
  • What is a guess that is too high?
  • What is your best guess?
  • What information do we need to know to figure this out?

Background Information

This sink hole was amazing because of its size but also how cylindrical it was. Here are a few other articles so you can find out more – article 1 & article 2. The two videos below will also help to give you an idea of the size of the whole

Get your measuring tapes out – How big is the hole?

There are differing reports on how big the hole actually is:

  • National Geographic: “60 feet (18 meters) wide and about 30 stories deep” (assuming a story is about 10 feet, then about 300 feet deep)
  • Time Magazine: “runs some 200 ft. deep”
  • CNN: “The 20-meter (about 66 feet) diameter sinkhole is about 30 meters (about 100 feet) deep.”
  • Slate: “A sinkhole, 65 feet across and 100 feet deep”

Use these conclusions to help you come up with the dimensions of the hole:

  •  National Geographic, CNN, and Slate seem to agree that the diameter is about 20 meters, so that is what I will assume.
  • The depth measurement varies from 100 feet to 200 feet to 300 feet. Obviously that is a huge difference.
  • The pictures don’t seem to be helpful in determining the depth.
  • Looking at the video, the sinkhole looks to be a little more than 1.5 times deeper than it is wide. So, that seems to match up with the CNN and Slate measurements.

Once you have the dimensions you need to work out the volume and once you have done that you need to use this site to help to work out the cost (link here)

N.B. The prices on the above site are in Australian dollars and these won’t help in Guatemala if you have to pay local workers.

Bonus – Could a domino topple a skyscraper?

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