find the surface area of the cone in terms of pi.

Question

highschoolmom2010 · Answer

attachment

phi · Answer

can you write down the equation you should use ?

highschoolmom2010 · Answer

I can put the one I was given...

highschoolmom2010 · Answer

$$SA=LA+B$$

phi · Answer

yes, but what is the equation for LA  and for B ?

highschoolmom2010 · Answer

$$LA=\frac{ 1 }{ 2 }*2\pi(r)*l$$

highschoolmom2010 · Answer

B is supposed to be the base I think

phi · Answer

yes, and what is the formula for the area of the base?

highschoolmom2010 · Answer

im not sure

phi · Answer

the base is a circle.  What is the formula for the area of a circle?

highschoolmom2010 · Answer

oh ok $$A=r^2$$

highschoolmom2010 · Answer

so $$SA=\frac{ 1 }{ 2 }*2\pi(r)*l+r^2$$

phi · Answer

close.  when you see "circle" think $\pi$
Area of a circle = $ π r^2 $

So let's get organized. So far we have

$$ SA=LA+B \
SA= \pi r l + \pi r^2 $$

phi · Answer

notice that 1/2 * 2  simplifies to 1 in your LA formula

highschoolmom2010 · Answer

oj ok I see now

phi · Answer

now replace the letters with the numbers (from the figure)
can you do that ?

Because they want the answer "in terms of pi", (which means leave pi in the answer)
we could "factor out" the pi:
$$ SA= \pi r l + \pi r^2 \
SA = (r l + r^2) \pi $$

now replace the letters with the numbers (from the figure)
can you do that ?

highschoolmom2010 · Answer

$$SA=((12*18))+12^2)\pi$$
$$SA=(216+144 )\pi$$$$SA=360\pi$$


that doesnt look right though

highschoolmom2010 · Answer

@phi

phi · Answer

It looks good to me.

highschoolmom2010 · Answer

my book says it is 144 cm ^2 i dont see how

phi · Answer

The question 19 asks for the answer in terms of pi.
144 cm^2 is *not* in terms of pi... so it looks like it is the answer to a different problem.

highschoolmom2010 · Answer

^^ i forgot the pi part

highschoolmom2010 · Answer

http://www.coursesmart.com/SR/5548832/9781256493303/1012?__hdv=6.8

phi · Answer

if the radius were 6, we would get
$$ (6*18+ 6*6) π = (108+36)π = 144 π $$

so it looks like they are using a radius of 6.  The picture *seems* to show the radius is 12... I would say this is a lousy question if they cannot be clear about what is what !

highschoolmom2010 · Answer

ok so 12 is the diameter then.....!!!thats annoying

phi · Answer

Yes. This is supposed to be a course in math, not reading the mind of the goofy questioner.

highschoolmom2010 · Answer

thanks @phi  for clarifying that for me

highschoolmom2010 · Answer

that makes way more sense

phi · Answer

I would show this problem to your teacher, and complain that it is a lousy book.  Maybe they will choose a better one next time.

highschoolmom2010 · Answer

i sent that to her and told her that the book was not clear on what the values were for what she said she would look at it