Question

Would someone please help me with this? I just don't understand how to do it.
Janine made a cylindrical vase in which the sum of the lateral area and area of one base was about 3000 square centimeters. The vase had a height of 50 centimeters. Find the radius of the vase. Explain the method you would use to find the radius.

Answer 1

"the sum of the lateral area and area of one base was about 3000 square centimeters"

this means that if we add up the surface area of the sides and base it = 3000

so, surface area of the sides = 2*pi*r*h
and surface area of base = pi*r^2

this means that:

3000 = 2*pi*r*h + pi*r^2

we know that h= 50 so,

3000 = 100*pi*r + pi*r

taking pi to be 3.14:

3000 = 314*r + 3.14r

3000 = 317.14*r

r = 9.46 cm (estimation)

Answer 2

oops wait i forgot a ^2 in there

Answer 3

3000 = 100*pi*r + pi*r^2

taking pi to be 3.14:

3000 = 314*r + 3.14r^2

setting = 0

3.14r^2 + 314r -3000 = 0

we must use the quadratic formula:

\[\frac{ -314 \pm \sqrt{314^{2}-4(3.14)(-3000)} }{ 2(3.14) }\]

Answer 4

Umm What's a setting?

Answer 5

which gives:

r = 8.78 cm and r = -108.78 cm

but a negative radius doesn't make sense so:

r = 8.78 cm

Answer 6

*You're setting the equation equal to 0 in that step

Answer 7

But why?

Answer 8

@wolfgirl I'm not sure how to do it either. Want to work on it together?

Answer 9

Yes please

Answer 10

Okay. What class are you in? I mean how much do you know about Geometry?

Answer 11

@wolfgirl are you pressed for time, or can you take your time?

Answer 12

You there??

Answer 13

I'm so sorry! I was in the middle of something. I'm here now.

Answer 14

Okay.

Answer 15

I'm in this Geometry Class in Ashworth High School but it isn't my strongest subject.

Answer 16

What year? What do you know about geometry? A little. A lot. Sort of okay.

Answer 17

I'm in my senior year. I've basically gone through the entire class and I'm working on my finals. I know the most of the formulas and stuff.

Answer 18

You know more than I do.

What was it about Piglet's explanation that you didn't understand?

Answer 19

Haha Well I don't understand what a setting is or what it's used for...

Answer 20

Okay. Let me read what he wrote.

Answer 21

Let's forget about Piglet.

What's a lateral?

Answer 22

Umm I believe that a lateral is the sum of all the faces

Answer 23

I think you're going to need to be certain about that, aren't you?

How much time do you have?

Answer 24

I have plenty of time

Answer 25

Okay. Maybe we should be working from the same textbook.

I'll give you the link to some free ones.

Answer 26

Okay, thank you

Answer 27

http://opencoursescholar.wordpress.com/resources/openstax-textbooks/

Go down to geometry and click on that. Then when you're on the page, click on flexbooks.

Answer 28

Okay. There

Answer 29

There are two books that I recommend. One is Geometry Concepts and the other is Geometry 2

Answer 30

I mean once you're on the Flexbooks page.

Answer 31

Okay, I'm on Geometry Concepts

Answer 32

Download it as a PDF

Answer 33

That way you'll have it whenever you need it. There are link in the books that you can click on that will take you to videos, and widgets, and so forth.

Answer 34

Don't worry if you're having any trouble. That always seems to happen to me. Maybe I can help if you are having any.

Answer 35

I'm downloading it

Answer 36

Okay cool. Once you get that one, get the Geometry 2.

I also found a video that you might like.

Are you familiar with the Khan Academy?

Answer 37

http://www.youtube.com/watch?feature=player_embedded&v=gL3HxBQyeg0

Answer 38

I am not familiar with them

Answer 39

Okay. Well, you have time to relax and find out more about your available resources as time goes by.

I found out that as you mentioned, they probably are talking about "lateral surface area".

http://ncalculators.com/area-volume/cylinder-calculator.htm

Answer 40

The link that I gave you earlier is for my blog. You'll find tons of excellent stuff there. So place the link some place that's handy for you.

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CC4QFjAA&url=http%3A%2F%2Fopencoursescholar.wordpress.com%2F&ei=-zRxUosM08-wBITdgcAN&usg=AFQjCNH-TGaxkrFCTIdwjft_MAhpTj_qKQ&sig2=agqJZEGG5ZDzRw8TJqqzyw&bvm=bv.55617003,d.cWc

Answer 41

http://opencoursescholar.wordpress.com/

Above is the short version of the same link

Answer 42

Thank you
Well the problem was basically the fact that the number 3000 was the lateral area plus the area of one of the bases and I needed to find the radius. I was supposed to use the quadratic formula to find it. I'm not sure what that is though.

Answer 43

You'll be using the quadratic formula A LOT!!!!!

Are you planning on going to college?

Answer 44

uhh yeah, I guess so

Answer 45

Well, even if you do independent studies, you'll need this stuff. Some folks don't have the funds for college, but these days you can still study it.

Answer 46

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&ved=0CEIQjBAwAg&url=http%3A%2F%2Fwww.ck12.org%2Falgebra%2F&ei=rTZxUsjrFfXKsQTz9IB4&usg=AFQjCNE_zXhSxrglizDeDHVuCA7MM9U4ww&sig2=HhlmfVoVqOYxwbMEulUZgQ&bvm=bv.55617003,d.cWc

That's the link to the algebra textbooks that have the quadratic formula in it.

Answer 47

Okay, thanks. If I go to college, my parents are paying for it because I don't wanna go...they're making me.

Answer 48

You'll probably be glad you went. Beats working at McDonalds. :)

Answer 49

Here's a link to the quadratic formula

http://www.ck12.org/algebra/Quadratic-Formula/

Answer 50

Haha, and thanks

Answer 51

You're very welcome.

Answer 52

So, where are you at with this problem? That one link really has good stuff. The one with the applet.

Answer 53

I think I've figured it out, it's more simple than I thought.

Answer 54

Okay. Anything else you need?

Answer 55

Nope, that'll be it :) Thank you so much!

Answer 56

You're welcome. Good luck with the test. :)

Answer 57

Thanks, I'll need it.