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Estimating Surface Area

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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)

Cone

- Simple shapes can be used to estimate the surface area of more complicated 3-D objects
- What shape do you think we should use?

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?

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?

The cylinders are obviously larger than the cone

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

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?

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

This gives a much closer estimate than our first approach

There is a formula for surface area of a cone

Is there a formula for this shape?

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

- What do you think we should do?

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