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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) Estimating the Surface Area of 3-D Objects Cone
Model Your 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?
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
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
The cylinders are obviously larger than the cone Do you think this is more accurate? How do you know? Over Estimating
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
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?
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? More Complicated Shapes
More complicated shapes • What do you think we should do?
This looks pretty good… • Don’t forget, not all the surface area of the boxes needs to be counted.