# Math Help - Surface Area basic

1. ## Surface Area basic

hai...

i have confusing in order to get the ans for the following attached problem. i already attached the my ans.

the correct ans from book: 659.82 $cm^2$

2. Hey,

So the surface area of a cylinder is:

$SA_{cyl} = 2\pi r^2 + 2\pi rh$

Since we are taking off the top of the cylinder we can change it to:

$SA_{cyl} = \pi r^2 + 2\pi rh$

Next we need the surface area for a cone, minus the area of the base of the cone.

$SA_{cone} = \pi rs + 2\pi r^2$

Again, we don't need the base of the cone, so we get:

$SA_{cone} = \pi rs$

This formula requires a value 's' which is the diagonal length (straight dotted line in your picture). We get this from Pythagoras.

$s^2 = h^2 + r^2 \Rightarrow s = \sqrt{12^2 + 5^2} = 13$

There we are! We have everything we need. So, the surface area of our modified cylinder is:

$SA_{mod} = SA_{cyl} + SA_{cone} = (\pi r^2 + 2\pi rh) + (\pi rs)$
$SA_{mod} = (\pi 5^2 + 2\pi(5)(12)) + (\pi (5)(13)) = 660 cm^2$

At least, that's what I get. Hope it helps!
--
Dave

3. if i not mistaken the surface area of cone is SA_{cone} = \pi rs + \pi r^2