anonymous
  • anonymous
The two cylinders are similar. If the ratio of their surface areas is 9/1.44, find the volume of each cylinder. Round your answer to the nearest hundredth.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
A. small cylinder: 152.00 m3 large cylinder: 950.02 m3 B. small cylinder: 972.14 m3 large cylinder: 12,924.24 m3 C. small cylinder: 851.22 m3 large cylinder: 13,300.25 m3 D. small cylinder: 682.95 m3 large cylinder: 13,539.68 m3
anonymous
  • anonymous
Please hurry
hartnn
  • hartnn
Surface area is proportional to square of the dimensions (radius and height). where as Volume is proportional to cube of dimensions!

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hartnn
  • hartnn
so lets show how we came upto that larger radius R = kr (k is constant, r is smaller radius) larger Height H = kh, h= smaller height. now Ratio of surface area = large surface area/ smaller surface area. = 2piR (R+h) / 2pi r (r+h) = kr(kr+kh)/(r(r+h)) = k^2 and this is given to be 9/1.44 k^2 = 9/1.44, so first find the value of k!
anonymous
  • anonymous
I am so confused.. im sorry i have no idea how to do this
anonymous
  • anonymous
What is k?
hartnn
  • hartnn
k is the constant of proportionality . since the cylinders are similar, their sides will be proportional that why i could take R/r = k k is some constant
hartnn
  • hartnn
and H/h = k
hartnn
  • hartnn
once we find k, we can find the ratio of volumes! larger volume/ smaller volume = pi R^2 * H / pi r^2 * h = k^2 r^2 (kh) / r^2 h = k^3 so ratio of volume is just k^3 !
anonymous
  • anonymous
is K 2.5
anonymous
  • anonymous
?
hartnn
  • hartnn
yep, thats correct :)
anonymous
  • anonymous
The answer is D. Get it over with.
anonymous
  • anonymous
hahaha well thanks!
anonymous
  • anonymous
You take 9/1.44 square root it then cube it (to find the constant so to speak) then you divide all the given values to see which one fits the constant. Move on!
hartnn
  • hartnn
so Jack, you say the volume ratio for D is 15.625 ?? can you double check? :P
anonymous
  • anonymous
The answer isnt d than?
hartnn
  • hartnn
as we found that volume of ratio is k^3 which is 2.5^3 = 15.625 now you just check volume ratio for each option and the one which gives you 15.625 is your answer :)
hartnn
  • hartnn
ratio of volume** not volume of ratio :P
anonymous
  • anonymous
Oh damn I meant C
anonymous
  • anonymous
sorry. Sloppy reading.
hartnn
  • hartnn
I am sure you meant C :)
anonymous
  • anonymous
I read it off wrong (hang's himself)
hartnn
  • hartnn
because your method was correct :)
hartnn
  • hartnn
karissa, what is the volume ratio of option C?? is it 15.625??
anonymous
  • anonymous
yeah I checked...
hartnn
  • hartnn
let her check lol its her question !
anonymous
  • anonymous
If she was at all committed to the question, she'd go to a quiet area with 20 text books and lock herself from human civilisation to come up with the answer and on the way perhaps prove fermat's last theorem.
hartnn
  • hartnn
oh well.... true that!

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