S=2 pi r^2 + 2 pi r h
pi is the symbol, 3.141..............
r is radius
h is height
a rewrite the formula to describe the total surface area for all cylinders with a height of 10 cm.
Now, suppose you were only considering cylinders with a height of 10 cm. What sort of substitution should you make here? Your new formula should relate the surface area directly to the radius, since the height is fixed.
The new formula should deal only with cylinders that have a height of 10 cm. In our given formula, represents height, so all we have to do is substitute 10 cm for to produce another formula that only works with cylinders of that height. Do you see?
We have with so , and you can simplify from there.
Now, try to do the factoring on your own: all you have to do is find the common factors of each term, and pull them out of the expression. For example, factors as follows:
Each term has a factor of , so we can pull it out as a factor of the whole expression. Now, you try!