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Estimating Surface Area. The art of math…. You can’t always get an exact answer when looking for the surface area of a complex 3-D shape We use estimation methods to get an approximate answer We will demonstrate this with a cone (even though there is a formula available).

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Estimating surface area

Estimating Surface Area

The art of math…


Estimating the surface area of 3 d objects

You can’t always get an exact answer when looking for the surface area of a complex 3-D shape

We use estimation methods to get an approximate answer

We will demonstrate this with a cone (even though there is a formula available)

Estimating the Surface Area of 3-D Objects

Cone


Model your shape
Model Your Shape surface area of a complex 3-D shape

  • Simple shapes can be used to estimate the surface area of more complicated 3-D objects

  • What shape do you think we should use?


Estimating with cylinders

This will provide an estimate by using a shape we are more familiar with

If we only use the sides of the cylinder will this is an over or under estimate?

Estimating with cylinders


It was an underestimate

You can see from the “net” that the cone had more surface area than the cylinders

What happens to our estimate if we use larger Cylinders?

It was an underestimate


Over estimating

The cylinders are obviously larger than the cone surface area than the cylinders

Do you think this is more accurate? How do you know?

Over Estimating


Over estimating1

What if we averaged our results? Or tried cylinders a little smaller than these but bigger than the first set?

What else could we try?

Over Estimating


What happens if you increase the number of cylinders

This is still an underestimate, BUT it is a better model for the cone

This gives a much closer estimate than our first approach

What happens if you increase the number of cylinders?


More complicated shapes

There is a formula for surface area of a cone the cone

Is there a formula for this shape?

What shape should we use to calculate the surface area of this one?

More Complicated Shapes




More complicated shapes1
More complicated shapes estimate!

  • What do you think we should do?


This looks pretty good
This looks pretty good… estimate!

  • Don’t forget, not all the surface area of the boxes needs to be counted.


Your turn
Your Turn! estimate!


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