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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.
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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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0hint: 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

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0please you have to solve that equation for x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i didnt how you got yhe equation *the

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0the sum of the volumes of the 2 spheres, has to be equal to the volume of the starting cone

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 4 }{ 3 }\pi (R^3 + r^3) = \frac{ 1 }{ 3 }\pi(r^2h)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0not 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03 and pi get cancelled?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0more precisely: \[\Large 4\left( {{R^3} + {x^3}} \right) = {r^2}h\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we have to divide both sides by 4

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0ok! now we have subtract R^3 at both sides

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0finally we have to take the 3rd root of both sides

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0you should get this: \[\Large x = \sqrt[3]{{\frac{{{r^2}h}}{4}  {R^3}}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0\[\Large x = \sqrt[3]{{\frac{{{r^2}h}}{4}  {R^3}}} = \sqrt[3]{{\frac{{{6^2} \cdot 21}}{4}  {4^3}}} = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0that's right! x= 5 cm
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