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mcsuds
 one year ago
Find the largest possible volume of a cone that fits inside a sphere of radius one.
mcsuds
 one year ago
Find the largest possible volume of a cone that fits inside a sphere of radius one.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you get the volume of the sphere which is 4.18879

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then you just have to find a volume of a cone smaller than that

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.0Use the above diagram and find an equation to represent the volume of the cone in terms of r. Then you can get the answer :)

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.2Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 3? Let R = radius sphere r = base radius cone R + h = height cone V = volume cone _______ V = (1/3)πr²(R + h) By the Pythagorean Theorem: r² = R²  h² Plug into the formula for volume. V = (1/3)π(R²  h²)(R + h) = (1/3)π(R³ + R²h  Rh²  h³) Take the derivative and set equal to zero to find the critical points. dV/dh = (1/3)π(R²  2Rh  3h²) = 0 R²  2Rh  3h² = 0 (R  3h)(R + h) = 0 h = R/3, R But h must be positive so: h = R/3 Calculate the second derivative to determine the nature of the critical points. d²V/dh² = (π/3)(2R  6h) < 0 So this is a relative maximum which we wanted. Solve for r². r² = R²  h² = R²  (R/3)² = R²(1  1/9) = (8/9)R² Calculate maximum volume. V = (π/3)[(8/9)R²](R + R/3) = (8/27)πR³(4/3) = 32πR³/81 For R = 3 maximum volume is: V = 32π(3³)/81 = 32π(27)/81 = 32π/3

madhu.mukherjee.946
 one year ago
Best ResponseYou've already chosen the best response.2this was the question that came in our examination and this is how i solved it ....and this is similar to your problem only difference is that you gotta put 1 in place 3 (radius):))))))
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