I dont understand what this question is asking me.  Is the answer just 2197:8000 Then I dont know what to do with the other two equations r1/r2=h1/h2=a/b=?  Am I supposed to find the ratios and...

I dont understand what this question is asking me.  Is the answer just 2197:8000

Then I dont know what to do with the other two equations r1/r2=h1/h2=a/b=? 

Am I supposed to find the ratios and heights and fill it in?

Sorry if these questions are silly but I just moved and dont currently have my textbook

Asked on by rguthrie94

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

The ratio of the volumes of two right circular cylinders is given as 2197:8000.

All right circular cylinders are similar -- their bases are circles and all circles are similar.

For similar figures, if the scale factor is a:b, then all corresponding linear measurements are in the ratio of a:b. All corresponding areas are in the ratio a^2:b^2, and corresponding volumes are in the ratio a^3:b^3.

Since the volumes are in the ratio 13^3:20^3:

V1:V2=2197:8000

A1:A2=13^2:20^2=169:400

S1:S2=13:20; in particular, the ratio of radii and the ratio of the heights will be 13:20

nick-teal's profile pic

nick-teal | High School Teacher | (Level 3) Adjunct Educator

Posted on

We can set up two formulas to represent the volumes of the cylinders.

`pi (r_1)^2 * h_1 = 2197 pi`

`pi (r_2)^2 h_2 = 8000 pi`

Then to find ratios, solve for the variables. 

For example `r_1 = sqrt(2197/h_1)`

Then we can solve for r_2 and turn that into a ratio.

gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

You have to find all the ratios:

Ratio of volumes

Ratio of areas

and ratio of heights, radii, etc. 

Use the equation for volume of a cylinder (pi x r x r x h) for finding the ratio of other parameters..

hope this helps

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