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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
Surface area is proportional to square of the dimensions (radius and height). where as Volume is proportional to cube of dimensions!
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!
I am so confused.. im sorry i have no idea how to do this
What is k?
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
and H/h = k
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 !
is K 2.5
yep, thats correct :)
The answer is D. Get it over with.
hahaha well thanks!
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!
so Jack, you say the volume ratio for D is 15.625 ?? can you double check? :P
The answer isnt d than?
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 :)
ratio of volume** not volume of ratio :P
Oh damn I meant C
sorry. Sloppy reading.
I am sure you meant C :)
I read it off wrong (hang's himself)
because your method was correct :)
karissa, what is the volume ratio of option C?? is it 15.625??
yeah I checked...
let her check lol its her question !
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.
oh well.... true that!