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anonymous

  • one year ago

A solid cone of radius 6 cm and height 21 cm is melted and made into 2 spheres of different sizes.The radius of the first sphere is 4 cm , find the radius of the second sphere.

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  1. anonymous
    • one year ago
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    @Michele_Laino

  2. Michele_Laino
    • one year ago
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    hint: the volume of the 2 spheres has to be equal to the volume of the starting cone, so we can write this equation: \[\Large \frac{{4\pi }}{3}{R^3} + \frac{{4\pi }}{3}{x^3} = \frac{{\pi {r^2}h}}{3}\] where x is the requested radius, R=4 cm, h=21 cm, and r= 6 cm

  3. anonymous
    • one year ago
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    ???

  4. Michele_Laino
    • one year ago
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    please you have to solve that equation for x

  5. anonymous
    • one year ago
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    i didnt how you got yhe equation *the

  6. Michele_Laino
    • one year ago
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    the sum of the volumes of the 2 spheres, has to be equal to the volume of the starting cone

  7. anonymous
    • one year ago
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    \[\frac{ 4 }{ 3 }\pi (R^3 + r^3) = \frac{ 1 }{ 3 }\pi(r^2h)\]

  8. Michele_Laino
    • one year ago
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    not exactly, better is: \[\Large \frac{{4\pi }}{3}\left( {{R^3} + {x^3}} \right) = \frac{{\pi {r^2}h}}{3}\] where x is the requested radius, and r is the radius of the starting cone, namely r= 6 cm

  9. anonymous
    • one year ago
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    3 and pi get cancelled?

  10. Michele_Laino
    • one year ago
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    yes!

  11. anonymous
    • one year ago
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    r^h = 4(R^3 + x^3)?

  12. Michele_Laino
    • one year ago
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    more precisely: \[\Large 4\left( {{R^3} + {x^3}} \right) = {r^2}h\]

  13. anonymous
    • one year ago
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    what next?

  14. Michele_Laino
    • one year ago
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    we have to divide both sides by 4

  15. anonymous
    • one year ago
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    (R^3 +x^3) = r^2h/4

  16. Michele_Laino
    • one year ago
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    ok! now we have subtract R^3 at both sides

  17. anonymous
    • one year ago
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    x^3 = r^2h/4 - R^3

  18. Michele_Laino
    • one year ago
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    finally we have to take the 3-rd root of both sides

  19. anonymous
    • one year ago
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    ???

  20. Michele_Laino
    • one year ago
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    you should get this: \[\Large x = \sqrt[3]{{\frac{{{r^2}h}}{4} - {R^3}}}\]

  21. anonymous
    • one year ago
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    ok!

  22. Michele_Laino
    • one year ago
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    \[\Large x = \sqrt[3]{{\frac{{{r^2}h}}{4} - {R^3}}} = \sqrt[3]{{\frac{{{6^2} \cdot 21}}{4} - {4^3}}} = ...?\]

  23. anonymous
    • one year ago
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    5?

  24. Michele_Laino
    • one year ago
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    that's right! x= 5 cm

  25. anonymous
    • one year ago
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    thanks.

  26. Michele_Laino
    • one year ago
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    :)

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