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.
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.
You are given a formula: $\displaystyle S=2\pi r^2 + 2\pi rh$. With this formula, you can find the surface area $\displaystyle S$ of any cylinder, provided that you substitute the radius for $\displaystyle r$ and the height for $\displaystyle h$. So, for example, if I have a cylinder of radius 5 cm and height 6 cm, its surface area would be:
$\displaystyle S=2\pi r^2 + 2\pi rh=2\pi (5)^2 + 2\pi (5)(6) = 110\pi\approx 345.58\text{ cm}^2$.
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.
Once you come up with your new formula, find the common factors in each term, and factor them out.
You can't figure it out?
The new formula should deal only with cylinders that have a height of 10 cm. In our given formula, $\displaystyle h$ represents height, so all we have to do is substitute 10 cm for $\displaystyle h$ to produce another formula that only works with cylinders of that height. Do you see?
We have $\displaystyle S=2\pi r^2 + 2\pi rh$ with $\displaystyle h=10\text{ cm}$ so $\displaystyle S=2\pi r^2 + 2\pi r(10)$, 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, $\displaystyle 3x^3 + 27x^2 - 9x$ factors as follows:
$\displaystyle 3x^3 + 27x^2 - 9x$
$\displaystyle =3(x)(x^2) + (3)(9)(x)(x) - (3)(3)x$
$\displaystyle =(3x)(x^2) + (3x)(9x) - (3x)(3)$
$\displaystyle =(3x)(x^2 + 9x - 3)$
Each term has a factor of $\displaystyle 3x$, so we can pull it out as a factor of the whole expression. Now, you try!