Help needed from those who are good in math

I need some help with 2 math problems from my math class. I used to be good in math, and still am, in some areas, like probability, which I can use in poker, but not so much in other areas, like geometry.

I have until Tuesday to turn these in, so if anyone can help, and explain, it would be greatly appreciated.

1. A steel drum in the shape of a right circular cylinder is required to have a volume of 100 cubic feet.

a) express the amount of material needed to make the cylinder as a function of the radius

b) what radius gives the least amount of material?

c) what is the least amount of material needed for such a radius?

2. A sprinkler that sprays water in a circular motion is to be used to water a square garden. If the area of the garden is 920 sq. ft. find the smallest whole number radius that the sprinkler can be adjusted to so that the entire garden is watered. Also determine how much area outside the garden is watered?

If you can help, please do, and don't just give me the answer, please explain as well.

Thanks

Lol...
Am I reading correctly that you would like us to do your homework for you?
I can give you a hint.
On the first one- Minimizing the surface area of a container for a given volume means getting it as close to spherical as possible.
The second- The key to solving it is that the diagonal of the square garden will be the diameter of the circle. Find the dimensions of the garden. It's simple trig from there out.

Quote:

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Originally Posted by stinkyattic

It's simple trig from there out.

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Now that's an oxymoron--"simple trig"--lol.

No, I don't want you to do ALL my homework. I did the rest of it, but I just had issues with these 2 problems.

I just thought I would try here before going to a "homework helpsite", because the cannabis users here are SOOO knowledgable. kiss [insert ass here] lol

Just don't get geometry--never have--never will.

The first one. (a b and c)

This is the formula for the volume
Area of the circle*height=100
(pi*r^2)*h = 100

Solving for Height to get everything in terms of radius.
100/(pi*r^2) = h

Formula for Surface Area(material):
Circumference*height + 2(area of the circle)
h(2r*pi) + 2(pi*r^2)

Plug in your value of h from above.
(100/(pi*r^2))(2r*pi)) + 2(pi*r^2) = SA

Differentiate that. Solve for 0. Find the minimum. Then plug it in.

I think. Been a while and am doing it in my head.




edit: explanations

Differentiation turns out to be:
(-200/r^2) + 4*pi*r = dSA

Set it to 0
(-200/r^2) + 4*pi*r = 0

Solve for r
0 = 4*pi*r - 200/r^2
0 = pi*r - 50/r^2
0 = (pi*r^3 - 50)/r^2
0 = pi*r^3 - 50
r^3 = 50/pi
r = (50/pi)^(1/3)

Now this part I'm not typing out all the steps because its annoying. But you have the radius but you need the height. So you solve this:
h = 100/(pi*r^2)
h = (100/pi)/((50/pi)^(1/3))2

Take my word for it it breaks down into:
h = 2 * (50/∏)^(1/3)
h = 2 * r
h = 2r

Then plug it all back into the original and simplify:
M = 2*pi*r*h + 2*pi*r^2
M = 4*pi*r^2 + 2*pi*r^2
M = 6*pi*r^2
M = 6pi[(50/∏)^(1/3)]2

And thats it.

Enjoy doing your second problem.

Dude, I'm 24 and that looks like gibberish to me!

Thanks 2 ReUp 4 the info. I am going to make an attempt at understanding it now, I think it may be possible with your information, and the TI-83.

Thanks to stinkyattic 4 the hints.

The 2nd one is really really easy.
x^2 = 920
x = 31 or something
920 + 920 = c^2
C= square root of 1840 = also the diameter
radius = square root of 1840 divided by 2
pi * r^2 = total area sprinkled
total area sprinkled minus 920 is your answer to the 2nd part.

Sorry I wrote this up real quick its not extremely clear. Ask any questions you have and I'll clarify.

Quote:

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Originally Posted by ceecee79

I need some help with 2 math problems from my math class. I used to be good in math, and still am, in some areas, like probability, which I can use in poker, but not so much in other areas, like geometry.

I have until Tuesday to turn these in, so if anyone can help, and explain, it would be greatly appreciated.

1. A steel drum in the shape of a right circular cylinder is required to have a volume of 100 cubic feet.

V=(pi)(radius^2)(height) so substitute for Volume as 100 and
100 = (pi)(radius^2)(height)

a) express the amount of material needed to make the cylinder as a function of the radius

All your doing here is solving for variables: r(adius) or h(eight)
100
(pi)(h) = r(adius) ^2

With the answer you get from above, square root the answer, and that is the function for r.

b) what radius gives the least amount of material?
Use your brains and calculate it out just punching numbers basically to solve for the V=100

c) what is the least amount of material needed for such a radius?
See B

2. A sprinkler that sprays water in a circular motion is to be used to water a square garden. If the area of the garden is 920 sq. ft. find the smallest whole number radius that the sprinkler can be adjusted to so that the entire garden is watered. Also determine how much area outside the garden is watered?
Square garden. So a square has 4 equal sides, and the equation for the area of a square is s(ide) squared.

Area of a circle equation : (pi)(radius squared)

If you can help, please do, and don't just give me the answer, please explain as well.

Thanks

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See Above

To Continue my post above:

You should draw all this out as a point in the middle of square surrounded by a circle. The circle is touching the corners of the square.

Area of a circle equation is (pi)*radius^2

Side of the square from the garden is square root of 920. That number is 30 since this is all whole number work.
To find the radius of the circle, we can assume since this figure is a square garden that if two intersecting lines went through the center the angles formed at the center would be 90 degrees(right angles) to each other. This forms 4 triangles in the square. You can the use the "sine" functino for this problem.
In a right triangle, there is a 90* angle, and two 45* angles. Match these up. Sine is opposite side over the hypotenuse.
The longest side has the greatest angle.

So its' sin(45*) = X/30.
.707 = X/30
X = (.707)(30) = 22

So the radius equals 22 and that the shortest radius one can have to water the whole garden.

TO Find the area that is not being watered but is just extra, it's the area of the circle MINUS the area of the square garden.

Area of Circle = (pi)(radius^2)
Area of Square = side^2

so it's (3.14)(21^2) - 30^2 = 485 square feet not being watered

There you go my man. It's not about derivatives at this level, use the easy math for easy problems.

If it was a harder problem, then use the calculus.

Dave

"b) what radius gives the least amount of material?
Use your brains and calculate it out just punching numbers basically to solve for the V=100"

OK, YA.

1 + 1 = Jello

Ha im glad im not at school anymore. Btw that kind of question in a maths class makes me think you are still at high school and aint 18 years old, naughty naughty.

Damn, why does everyone seem to think I am in high school cause I ask a math question? There must be many here who are proficient in geometry in their adult lives. Oh well, I am not. Didn't get it then, still don't get it now. I am 28 years old, and in a college level MAT 140 class. Don't worry, I will direct any further questons to a homework helpsite to avoid any further issues. But just so you know........there are people past 18 who are still in school, usually it is called college, and not everyone is great at every subject there is.

To those who have offered assistance, without assuming I am under 18--thank you very much, it is much clearer now, and I appreciate it very much, especially since some of the responses looked time consuming.

BTW, I currently have a 4.0 GPA, and would like to keep it that way, which is why I asked for help. Additionally I know there are some very knowledgeable people on this site, and thought I may be able to receive more assistance than our ambiguous instructor could provide.

Im sorry, didnt mean to offend

Is okay, wasn't really U. It's just that was not the 1st comment I got where it was assumed I was still in high school. Didn't mean to rant too much.