Cylinder help..if the volume of a cylinder is 340 how do i find the perimeter, surface aria, and the hight

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- anonymous

You know that the Surface Area equation of a cylinder right? which is:\[SA = 2\pi r^2 + 2\pi r H\]
and the volume is :
\[V = \pi r^2 H\]
Perimeter is :
\[P = 2\pi R\]
all you have to do is find a relationship between all of them and you'll be able to figure out the height, perimeter and SA , so you'll get :
Notice that the volume is = pi r ^2 h and the perimeter is = 2pi r so the SA can be written as :
\[SA = 2(340)H + PH\]

- anonymous

are you sure that that's the only given?

- anonymous

yep i am givin x 1-a2 i think that is the radious and i have to find all of those for numbers 1-12

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- anonymous

x = 1- a2?

- anonymous

you need more given, I doubt that the only given is the volume lol

- anonymous

ok so the whole thing is a project we have to figure out what is best for making a box..we are given x values 1-12 and the volume of 340 cubic inches 1-12 i believe are the radices

- anonymous

i need to find the hight. the surface aria..and the perimeter of a cylinder

- anonymous

with that info

- anonymous

Alright, pick one of the radiuses and plug it in the Volume's equation to find H :) see if the number makes sense.

- anonymous

ok so i take piXr squared and get the hight?

- anonymous

for example .3.14X1 squared?

- anonymous

V = pi r^2 H , you can plug in any value or R, then find H, and after finding H you can plug it in the perimeter, and when you find the perimeter you'll be able to find the SA, the new equation that I have wrote up there ^_^

- anonymous

as far as I can go lol, since I don't have enough given

- anonymous

im not getting how you find h when you need it in the equation

- anonymous

alright, we have the volume right? :)

- anonymous

\[V = 340 \]

- anonymous

you have values of x, which are considered as the radius right?

- anonymous

so you can take R = 4 for example and plug it in the following equation:\[V = \pi r^2h\]
so we have R and V, we can solve for H, right?

- anonymous

lol, are you getting the idea now? :)

- anonymous

\[340=\pi(4) squared ?\]

- anonymous

actually it's :\[H = (340)/(8\pi)\]
and calculate it, that ofcourse if you choose your radius to be 4 ^_^ clear?

- anonymous

wait it's 32 pi instead of 8 pi I forgot to square it lol!

- anonymous

ok so i take x=340/r is this correct...if not i give up for the night and am going to bed..i am sure i am making this 100X harder than it actually is

- anonymous

and that will give me the hight ?

- anonymous

don't give up lol, alright, let's try once more!
WE have x values, right?

- anonymous

yes those values= the radius...so if the virst x value is 1 how do i get the hight?

- anonymous

it's simple, just take your time and concentrate with me

- anonymous

Okay so x = r = 1
we have given:
R = 1
V = 340
find H= ?

- anonymous

yep thats what i need to do...now how?

- anonymous

The equation is :
\[V = \pi r^2 h\]

- anonymous

plug in the given in the equation and solve for H :
340 = pi (1)^2 H
H = 340/pi
H = 108.23 in ^_^

- anonymous

we have found the height now :)

- anonymous

now we need to find the perimeter right?

- anonymous

are you following me lol? =P wakey wakey~

- anonymous

hold on

- anonymous

okay ^_^

- anonymous

ok so the hight for a radios of 1 is 108.2 correct

- anonymous

excellent!

- anonymous

ok so now perimeter

- anonymous

now, we can find the perimeter right? The equation is :
P = 2pi R
we have R = 1, solve :)

- anonymous

ok so i take \[2piX(1)squared\]

- anonymous

i got 6.28

- anonymous

lol no, the equation is :\[P = 2 \pi R\]
substitute R in the equation and you'll get P ^_^

- anonymous

lol yeah , that's right :)

- anonymous

now, we can find the SA right?

- anonymous

ok so now the SA

- anonymous

The equation is :\[SA = 2\pi r^2 + 2\pi r h\]
we have R = 1 and H = 108.2
substitute the given and solve ^_^

- anonymous

i got 686.1

- anonymous

very good !

- anonymous

you have solved the question using R = 1 ^_^
did you get the idea now? :)

- anonymous

ok let me make sure i can get this for 2 now and then ill let you go..if you dont mind

- anonymous

good morning

- anonymous

hi

- anonymous

alright, it's the same idea blackford, but different values for R ^_^, good morning andy

- anonymous

same way of solving , good luck! ^_^

- anonymous

i got 120.8

- anonymous

for?

- anonymous

the hight with a radios of 2

- anonymous

hmm it should be 27.06
(340)/(4pi) = H
H = 27.06 in

- anonymous

and andy going quite lol

- anonymous

oops i see i think..i just realized you want h by itself

- anonymous

yep ^_^ since we want to find it

- anonymous

ok for a R of 3 i got 12.02 for the hight..correct?

- anonymous

excellent ^_^

- anonymous

ok i think i am getting it now

- anonymous

you got the idea now :)

- anonymous

you can proceed on your own right?

- anonymous

for now thank you :)

- anonymous

np ^_^

- anonymous

i got a new one

- anonymous

alright

- anonymous

now for a square pyramid. this time i need the hight,perimeter, SA, and lateral aria

- anonymous

volume still 340 and same x values 1-12

- anonymous

All you have to do is write down the new equations for the square pyramid

- anonymous

i think that x= base length now

- anonymous

Volume is :
\[V = (b^2h)/3\]
Surface Area is :
\[SA = 2bs + b^2\]
and perimeter :
\[P = (\S-B)(1/2)(l)\]
find the relationship and solve ^_^ same idea as the previous one :)

- anonymous

P = (S-B)(1/2)(L) *

- anonymous

oh and the lateral area is = PL/2 where P = perimeter and L = slant height ^_^

- anonymous

ok so 340=1squared(h)/3

- anonymous

oh yeah i want the slant hight not lateral aria

- anonymous

so \[340=1^2(h).....340=1/3 =.33 340/.33..correct or no\]

- anonymous

340(3) = h
h = 1020

- anonymous

lol, I see what's your problem, you got the idea, but have trouble with calculation, take your time answering the questions :) step at a time ^_^

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