# How to find the total surface area S of a cylinder with radius r and height h can be

• May 3rd 2008, 06:57 PM
nppatel4428
How to find the total surface area S of a cylinder with radius r and height h can be
S=2 pi r^2 + 2 pi r h

pi is the symbol, 3.141..............
h is height
a rewrite the formula to describe the total surface area for all cylinders with a height of 10 cm.
• May 3rd 2008, 07:09 PM
Reckoner
Quote:

Originally Posted by nppatel4428
S=2 pi r^2 + 2 pi r h

pi is the symbol, 3.141..............
h is height
a rewrite the formula to describe the total surface area for all cylinders with a height of 10 cm.

Hi! What sort of difficulty are you having? A simple substitution will give you the correct formula.
• May 3rd 2008, 07:15 PM
nppatel4428
i dont get how u do it. what r u supposed to do?
• May 3rd 2008, 07:16 PM
nppatel4428
how do i rewrite the formula to describe the total surface area for all cylinders with a height of 10 cm. then how do i express that equation into factored form?
• May 3rd 2008, 07:27 PM
Reckoner
Quote:

Originally Posted by nppatel4428
i dont get how u do it. what r u supposed to do?

You are given a formula: $S=2\pi r^2 + 2\pi rh$. With this formula, you can find the surface area $S$ of any cylinder, provided that you substitute the radius for $r$ and the height for $h$. So, for example, if I have a cylinder of radius 5 cm and height 6 cm, its surface area would be:

$S=2\pi r^2 + 2\pi rh=2\pi (5)^2 + 2\pi (5)(6) = 110\pi\approx 345.58\text{ cm}^2$.

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.

Quote:

Originally Posted by nppatel4428
then how do i express that equation into factored form?

Once you come up with your new formula, find the common factors in each term, and factor them out.
• May 3rd 2008, 07:35 PM
nppatel4428
so whatwouldthe new formula be?
• May 3rd 2008, 07:50 PM
Reckoner
Quote:

Originally Posted by nppatel4428
so whatwouldthe new formula be?

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, $h$ represents height, so all we have to do is substitute 10 cm for $h$ to produce another formula that only works with cylinders of that height. Do you see?

We have $S=2\pi r^2 + 2\pi rh$ with $h=10\text{ cm}$ so $S=2\pi r^2 + 2\pi r(10)$, 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, $3x^3 + 27x^2 - 9x$ factors as follows:
$3x^3 + 27x^2 - 9x$
$=3(x)(x^2) + (3)(9)(x)(x) - (3)(3)x$
$=(3x)(x^2) + (3x)(9x) - (3x)(3)$
$=(3x)(x^2 + 9x - 3)$

Each term has a factor of $3x$, so we can pull it out as a factor of the whole expression. Now, you try!