If the scale factor of two similar solids is 4:17, what is the ratio of their corresponding area and volumes?
A. 4:289 and 17:4,913
B. 8:34 and 12:51
C. 16:289 and 64:4,913
D. 64:4,913 and 16:289
I am not sure of how to do this - please help...
I think the answer is A - please let e know if it is right.
area: 4^2/17^2
volume: 4^3/17^3
Now what is your answer?
its C for sure
To find the ratio of the corresponding areas and volumes of two similar solids, you need to use the cube of the scale factor.
Given that the scale factor is 4:17, let's call it x. We can write the scale factor as:
x = 4/17
To find the ratio of the corresponding areas, you need to square the scale factor. So the ratio of their areas is:
(x^2):(x^2) = (4/17)^2:(17/4)^2 = 16/289:289/16
And to find the ratio of the corresponding volumes, you need to cube the scale factor. So the ratio of their volumes is:
(x^3):(x^3) = (4/17)^3:(17/4)^3 = 64/4913:4913/64
So the correct answer is C. 16:289 and 64:4,913.