Question

How do I find the volume if I don't have the height????

Kent has two similar cylindrical pipes, Pipe A and Pipe B. The radius of Pipe A is 6 cm, and the radius of Pipe B is 2 cm. What is the ratio of the volume of Pipe A to the volume of Pipe B?

Answer 1

you dont need to find the volume...you just need the ratio

Answer 2

volume of pipe A is \[V_A = \pi r^2 h\]
\[\implies V_A = \pi (6)^2 h\]
\[\implies V_A = 36\pi h\]
agree?

Answer 3

Yes. The other will be v=pi(2)^2h which turns out to be v=4pih

Answer 4

right. so the ratio of pipe a to pipe b is \[\huge \frac{V_A}{V_B} \implies \frac{36\pi h}{4\pi h}\]
simplify that to get the ratio ;)

Answer 5

The h and the pi are going to cancel out then?

Answer 6

yup

Answer 7

So the answer is 9:1

Answer 8

correct you are

Answer 9

hmm....

Answer 10

if the solids are similar, then wouldn't the second height be 3 times larger than the first?

Answer 11

since every corresponding dimension is in proportion with each other

Answer 12

also, I'm thinking that the volume ratio should be 27:1 since 3^3 = 27

Answer 13

yes...i was wondering the same thing...it should be \[\frac{216}{8}\]
wonder where it went wrong...the h maybe @jim_thompson5910 ?

Answer 14

oops nvm, miscalculated

Answer 15

216/4 gives 54..

Answer 16

yeah my bad

Answer 17

you're right, 216/8 = 27

Answer 18

hmm...the ratio of volume is supposed to be the cube of the ratio of radii

Answer 19

so how would it look like algebraically?

Answer 20

maybe \[\huge V_A = \pi(6)^2 (3h)\]
and \[\huge V_B = \pi (2)^2(h)\]
??

Answer 21

The larger radius is 3 times the smaller radius (since 6/2 = 3)

So each dimension of the larger cylinder is triple its corresponding dimension

so if r1 and h1 are the radius and height of the smaller cylinder and r2 and h2 are the radius and height of the larger cylinder, then....

r2 = 3*r1

h2 = 3*h1

which makes the volumes to be

V1 = pi*(r1)^2*h1

V2 = pi*(r2)^2*h2

and the ratio of the volumes to be

(V2)/(V1) = (pi*(r2)^2*h2)/(pi*(r1)^2*h1)

but r2 = 3*r1 and h2 = 3*h1, which means we can say

(V2)/(V1) = (pi*(3*r1)^2*(3*h1))/(pi*(r1)^2*h1)

(V2)/(V1) = ((3*r1)^2*(3*h1))/((r1)^2*h1)

(V2)/(V1) = ((3*r1)^2*(3))/((r1)^2)

(V2)/(V1) = (9*(r1)^2*(3))/((r1)^2)

(V2)/(V1) = (9*3)/(1)

(V2)/(V1) = 27

Answer 22

So the ratio of the volumes is 27:1

Answer 23

yes, what you just wrote is exactly what I'm thinking

Answer 24

ahh yes...that's how it should be @tiffybabyy sorry for the mistake

Answer 25

your prev answer would work if the two heights were the same...but that would mean that the two solids aren't similar

Answer 26

hopefully I didn't needlessly complicate things for you tiffybabyy lol

Answer 27

Okay no I'm following.

Answer 28

alright, let me know if you get lost anywhere