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anonymous
 one year ago
What is the ratio for the volumes of two similar spheres, given that the ratio of their radii is 3:4?
A. 27:64
B. 16:9
C. 9:16
D. 64:27
anonymous
 one year ago
What is the ratio for the volumes of two similar spheres, given that the ratio of their radii is 3:4? A. 27:64 B. 16:9 C. 9:16 D. 64:27

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2the volume of the first sphere is: \[{V_1} = \frac{{4\pi }}{3}R_1^3\] whereas the volume of the second sphere is: \[{V_2} = \frac{{4\pi }}{3}R_2^3\] so if we divide side by side those formula each other, we get: \[\frac{{{V_1}}}{{{V_2}}} = \frac{{\frac{{4\pi }}{3}R_1^3}}{{\frac{{4\pi }}{3}R_2^3}} = {\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^3}\] now, we have: \[\frac{{{R_1}}}{{{R_2}}} = \frac{3}{4}\] so, please substitute that ratio into the expression for the ratio V_1/V_2, what do you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Michele_Laino I'm sorry if you should find be to be incompetent, seeing as how well this was explained, but I do not understand what it is I should be substituting in.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2it is simple, here is your substitution: \[\Large \frac{{{V_1}}}{{{V_2}}} = \frac{{\frac{{4\pi }}{3}R_1^3}}{{\frac{{4\pi }}{3}R_2^3}} = {\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^3} = {\left( {\frac{3}{4}} \right)^3} = ...?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Pretty sure my calculations are right.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep, double checked. Thank you @Michele_Laino! :)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2correct! @Thatsodan
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