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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

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  1. Michele_Laino
    • one year ago
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    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?

  2. Michele_Laino
    • one year ago
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    formulas*

  3. anonymous
    • one year ago
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    @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.

  4. anonymous
    • one year ago
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    *me to be

  5. Michele_Laino
    • one year ago
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    it is simple, here is your substitution: \[\Large \frac{{{V_1}}}{{{V_2}}} = \frac{{\frac{{4\pi }}{3}R_1^3}}{{\frac{{4\pi }}{3}R_2^3}} = {\left( {\frac{{{R_1}}}{{{R_2}}}} \right)^3} = {\left( {\frac{3}{4}} \right)^3} = ...?\]

  6. anonymous
    • one year ago
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    27/64

  7. anonymous
    • one year ago
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    Pretty sure my calculations are right.

  8. anonymous
    • one year ago
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    Yep, double checked. Thank you @Michele_Laino! :)

  9. dan815
    • one year ago
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    hello there dan :)

  10. Michele_Laino
    • one year ago
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    that's right!

  11. anonymous
    • one year ago
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    Hey dan :)

  12. Michele_Laino
    • one year ago
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    correct! @Thatsodan

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