Question

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.

Answer 1

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

Answer 2

Please hurry

Answer 3

Surface area is proportional to square of the dimensions (radius and height).
where as Volume is proportional to cube of dimensions!

Answer 4

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!

Answer 5

I am so confused.. im sorry i have no idea how to do this

Answer 6

What is k?

Answer 7

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

Answer 8

and H/h = k

Answer 9

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 !

Answer 10

is K 2.5

Answer 11

?

Answer 12

yep, thats correct :)

Answer 13

The answer is D. Get it over with.

Answer 14

hahaha well thanks!

Answer 15

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!

Answer 16

so Jack, you say the volume ratio for D is 15.625 ??
can you double check? :P

Answer 17

The answer isnt d than?

Answer 18

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 :)

Answer 19

ratio of volume**
not volume of ratio :P

Answer 20

Oh damn I meant C

Answer 21

sorry. Sloppy reading.

Answer 22

I am sure you meant C :)

Answer 23

I read it off wrong (hang's himself)

Answer 24

because your method was correct :)

Answer 25

karissa,
what is the volume ratio of option C??
is it 15.625??

Answer 26

yeah I checked...

Answer 27

let her check lol
its her question !

Answer 28

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.

Answer 29

oh well....
true that!