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