anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Michele_Laino
  • Michele_Laino
the 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?
Michele_Laino
  • Michele_Laino
formulas*
anonymous
  • anonymous
@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.

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anonymous
  • anonymous
*me to be
Michele_Laino
  • Michele_Laino
it 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
  • anonymous
27/64
anonymous
  • anonymous
Pretty sure my calculations are right.
anonymous
  • anonymous
Yep, double checked. Thank you @Michele_Laino! :)
dan815
  • dan815
hello there dan :)
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
Hey dan :)
Michele_Laino
  • Michele_Laino
correct! @Thatsodan

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