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) 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?

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?

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?

Over Estimating  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?

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

More Complicated Shapes  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?

Break the shape down!

Notice that we don’t need all if the area, it was an over estimate!

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.

Your Turn!